The Son of David and the Son of God

“…since the time that I commanded judges to be over My people Israel, and have caused you to rest from all your enemies. Also the Lord tells you that He will make you a house. When your days are fulfilled and you rest with your fathers, I will set up your seed after you, who will come from your body, and I will establish his kingdom. He shall build a house for My name, and I will establish the throne of his kingdom forever. I will be his Father, and he shall be My son. If he commits iniquity, I will chasten him with the rod of men and with the blows of the sons of men. But My mercy shall not depart from him, as I took it from Saul, whom I removed from before you. And your house and your kingdom shall be established forever before you. Your throne shall be established forever” (2 Samuel 7.11–16). 

David had many sons, both in his immediate family and among his descendants, but Israel recognized a special son of David, indicated by Second Samuel 7.

The connection between David and the Messiah is strong in the Old Testament:
Psa 89.35, 36
Psa 132.11
Isa 9.7
Isa 16.5
Isa 22.22
Jer 23.5
Jer 33.19–22
Eze 34.23, 24
Hos 3.5
Amos 9.11
Mic 5.2 (Bethlehem is the City of David)
Zec 13.1
Plus David wrote many psalms with a Messianic theme:
Psa 2
Psa 22
Psa 16
Psa 89
Psa 110
Psa 132
2Sa 23.1–7 and others

God promised David in Second Samuel 7 that this would last forever. Keil and Delitzsch say,

“The posterity of David, therefore, could only last for ever by running out in a person who lives for ever, i.e. by culminating in the Messiah, who lives for ever, and of whose kingdom there is no end” (p. 347). 

Fulfilled in these passages:

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The New Testament shows Jesus to be that special anointed son of David.
Matt 1.1
Matt 1.20
Matt 3.16, 17
Matt 9.27
Matt 12.23
Matt 15.22
Matt 20.30, 31
Matt 21.9
Matt 21.15
Matt 22.41–45
Luke 1.32, 33
Luke 3.31
Acts 2.25–36
Rom 1.1–4
Rev 5.5
Rev 22.16