All beings created directly from / by God Himself is called "sons of God". This includes

• Adam, the first human without human parents
• "angelic beings" (good and evil) that do not reproduce, all possibly directly created from / by God
• Christ, the only-begotten son of God
• adopted children, believers who are adopted as "sons" of God, for example:
  • Israel
  • King David

Adam

...he son of Enos, the son of Seth, the son of Adam, the son of God. -- Luke 3:38 (ESV)

"Angelic" beings

When man began to multiply on the face of the land and daughters were born to them, the sons of God saw that the daughters of man were attractive. And they took as their wives any they chose. Then the Lord said, “My Spirit shall not abide in man forever, for he is flesh: his days shall be 120 years.” The Nephilim were on the earth in those days, and also afterward, when the sons of God came in to the daughters of man and they bore children to them. These were the mighty men who were of old, the men of renown. The Lord saw that the wickedness of man was great in the earth, and that every intention of the thoughts of his heart was only evil continually. And the Lord regretted that he had made man on the earth, and it grieved him to his heart. So the Lord said, "I will blot out man whom I have created from the face of the land, man and animals and creeping things and birds of the heavens, for I am sorry that I have made them." -- Genesis 6:1-7 (ESV)

• These "sons of God" were not human.
• They could have sexual intercourse with human women.
• Note that the Nephilim themselves were never called "sons of God". They came into existence by disobedient "sons of God" and should have never existed.

Now there was a day when the sons of God came to present themselves before the Lord, and Satan also came among them. The Lord said to Satan, “From where have you come?” Satan answered the Lord and said, “From going to and fro on the earth, and from walking up and down on it.” -- Job 1:6-7 (ESV)

• They are not on Earth.
• They could present themselves to God during the time Job lived on Earth.

Now there was a day when his sons and daughters were eating and drinking wine in their oldest brother's house... -- Job 1:13

The same writer who wrote Job 1:6-7 who left out "daughters of God" now includes "daughters". This could potentially be understood that the "sons of God" does not have genders like humans.

Where were you when I laid the foundation of the earth? ... On what were its bases sunk, or who laid its cornerstone, when the morning stars sang together and all the sons of God shouted for joy? -- Job 38:4-7 (ESV)

• They already existed at the creation of Earth.
• They were happy about God's creation.

Angles

And Jesus said to them, “The sons of this age marry and are given in marriage, but those who are considered worthy to attain to that age and to the resurrection from the dead neither marry nor are given in marriage, for they cannot die anymore, because they are equal to angels [and] are sons of God, being sons of the resurrection. -- Luke 20:34-36 (ESV), Matthew 22:29-30

The word "and" in "angles and are sons of God" could also be translated as "angles namely sons of God".

• Angles cannot die.
• Angles do not marry like humans.

Babylonian understanding

He answered and said, “But I see four men unbound, walking in the midst of the fire, and they are not hurt; and the appearance of the fourth is like a son of the gods.” -- Daniel 3:25 (ESV)

• The king probably meant that he was seeing a supernatural being.

Christ

Christ is God's "only begotten" (born) Son (John 3:16 (NKJV), John 3:18 (NKJV), 1 John 4:9(NKJV)), because

• Adam was made directly by God and had no mother to give him birth (Genesis 2:7)
• Humans are "begotten" by human parents
• Believers are adopted by God (Romans 8:14,16-17)
• The angelic "sons of God" already existed before the Earth was created (Job 38:4-7)

Note that some Bible translations like the ESV omits the word "begotten". It is not true that Jesus is God's "only son". However, Jesus is God's "only begotten Son".

This was prophesied:

For to which of the angels did God ever say,

“You are My Son, today I have begotten you”?

Or again,

“I will be to him a father, and he shall be to me a son”?

-- Hebrews 1:5 (ESV), Psalm 2:7

It happened:

And the angel answered [Mary], "The Holy Spirit will come upon you, and the power of the Most High will overshadow you; therefore the child to be born will be called holy — the Son of God." -- Luke 1:35

For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life. -- John 3:16 (NKJV)

(Note some English bible translations leave out the word "begotton" which make no sense since God has many other "sons" too)

Adopted children of God

But when the fullness of the time had come, God sent forth His Son, born of a woman, born under the law, to redeem those who were under the law, that we might receive the adoption as sons. And because you are sons, God has sent forth the Spirit of His Son into your hearts, crying out, “Abba, Father!” Therefore you are no longer a slave but a son, and if a son, then an heir of God through Christ. -- Galatians 4:4-7 (NKJV)

Blessed are the peacemakers, for they shall be called sons of God. -- Matthew 5:9 (ESV)

Notice Jesus choose to introduce God as "your Father" and "our Father" which implies his audience are also considered children of his Father.

But I say to you, love your enemies and pray for those who persecute you, so that you may be sons of your Father who is in heaven. For he makes his sun rise on the evil and on the good, and sends rain on the just and on the unjust.

For if you love those who love you, what reward do you have? Do not even the tax collectors do the same? And if you greet only your brothers, what more are you doing than others? Do not even the Gentiles do the same?

You therefore must be perfect, as your heavenly Father is perfect.

Beware of practicing your righteousness before other people in order to be seen by them, for then you will have no reward from your Father who is in heaven.

Thus, when you give to the needy, sound no trumpet before you, as the hypocrites do in the synagogues and in the streets, that they may ube praised by others. Truly, I say to you, they have received their reward. But when you give to the needy, do not let your left hand know what your right hand is doing, so that your giving may be in secret. And your Father who sees in secret will reward you.

And when you pray, you must not be like the hypocrites. For they love to stand and pray in the synagogues and at the street corners, that they may be seen by others. Truly, I say to you, they have received their reward. But when you pray, go into your room and shut the door and pray to your Father who is in secret. And your Father who sees in secret will reward you.

“And when you pray, do not heap up empty phrases as the Gentiles do, for they think that they will be heard for their many words. Do not be like them, for your Father knows what you need before you ask him. Pray then like this:

"Our Father in heaven, hallowed be your name..."

-- Matthew 5:45-6:9 (ESV)

For if you forgive others their trespasses, your heavenly Father will also forgive you, but if you do not forgive others their trespasses, neither will your Father forgive your trespasses. And when you fast, do not look gloomy like the hypocrites, for they disfigure their faces that their fasting may be seen by others. Truly, I say to you, they have received their reward. But when you fast, anoint your head and wash your face, that your fasting may not be seen by others but by your Father who is in secret. And your Father who sees in secret will reward you. -- Matthew 6:14-18 (ESV)

Look at the birds of the air: they neither sow nor reap nor gather into barns, and yet your heavenly Father feeds them. Are you not of more value than they? And which of you by being anxious can add a single hour to his span of life?7 And why are you anxious about clothing? Consider the lilies of the field, how they grow: they neither toil nor spin, yet I tell you, even Solomon in all his glory was not arrayed like one of these. But if God so clothes the grass of the field, which today is alive and tomorrow is thrown into the oven, will he not much more clothe you, kO you of little faith? Therefore do not be anxious, saying, ‘What shall we eat?’ or ‘What shall we drink?’ or ‘What shall we wear?’ For the Gentiles seek after all these things, and your heavenly Father knows that you need them all. -- Matthew 6:26-32 (ESV)

If you then, who are evil, know how to give good gifts to your children, how much more will your Father who is in heaven give good things to those who ask him! -- Matthew 7:11

Then the righteous will shine like the sun in the kingdom of their Father. -- Matthew 13:43 (ESV)

Even so it is not the will of your Father who is in heaven that one of these little ones should perish. -- Matthew 18:14 (ESV)

This privilege was not limited to Jesus' direct disciples, but even Paul, who taught after Jesus ascended, reveled to his churches that they too are considered children of God:

For all who are led by the Spirit of God are sons of God. ... we are children of God, and if children, then heirs — heirs of God -- Romans 8:14,16-17 (ESV)

He predestined us for adoption to Himself as sons through Jesus Christ, according to the purpose of His will -- Ephesians 1:5 (ESV).

And I will be a father to you, and you shall be sons and daughters to me, says the Lord Almighty.” -- 2 Corinthians 6:18 (ESV)

One day God will reveal who are his adopted "sons".

For the creation waits with eager longing for the revealing of the sons of God. -- Romans 9:19 (ESV)

The one who conquers will have this heritage, and I will be his God and he will be my son. -- Revelations 21:7

Israel

Then you shall say to Pharaoh, ‘Thus says the Lord, Israel is my firstborn son, and I say to you, “Let my son go that he may serve me.” If you refuse to let him go, behold, I will kill your firstborn son.’” -- Exodus 4:22 (ESV)

Israel is the first humanly born nation that God called His "son". In this context God probably meant that as the Pharaoh loves his firstborn son, so God loves Israel.

Yet the number of the children of Israel shall be as the sand of the sea, which cannot be measured nor numbered; and it shall come to pass, that in the place where it was said unto them, Ye are not my people, there it shall be said unto them, Ye are the sons of the living God. -- Hosea 1:10 (KJV)

and

When Israel was a child, I loved him, and out of Egypt I called my son. -- Hosea 11:1 (ESV)

There is also the controversial verse in the "Song of Moses":

When the Most High gave to the nations their inheritance, when he divided mankind, he fixed the borders of the peoples according to the number of the sons of God

-- Deuteronomy 32:8 (ESV)

Some claim this is incorrectly translated:

King David

I will be to him a father, and he shall be to me a son. When he commits iniquity, I will discipline him with the rod of men, with the stripes of the sons of men, but my steadfast love will not depart from him. -- 2 Samuel 7:14-15 (ESV)