Romans 15:8 Now I say that Jesus Christ was a minister of the circumcision for the truth of God, to confirm the promises made unto the fathers:

Jesus, in his earthly ministry, came to confirm the promises made unto the fathers in regard to the earthly Davidic kingdom.

Romans15:9 And that the Gentiles might glorify God for his mercy; as it is written, For this cause I will confess to thee among the Gentiles, and sing unto thy name.

Paul is citing the verses below.

2 Samuel 22:50 Therefore I will give thanks unto thee, O LORD, among the heathen, and I will sing praises unto thy name.

Psalm 18:49 Therefore will I give thanks unto thee, O LORD, among the heathen, and sing praises unto thy name.

Paul is speaking not of the mystery of the Gentiles in the body of Christ, but the Gentiles in prophecy.

Romans 15:10 And again he saith, Rejoice, ye Gentiles, with his people.

Paul is citing from the verses below.

Deuteronomy 32:43 Rejoice, O ye nations, with his people: for he will avenge the blood of his servants, and will render vengeance to his adversaries, and will be merciful unto his land, and to his people.

Psalm 67:4 O let the nations be glad and sing for joy: for thou shalt judge the people righteously, and govern the nations upon earth. Selah.

God will judge his people, the believing remnant of Israel; the Gentiles will rejoice with his people and will sing of his mercies and righteous government.

Romans 15:11 And again, Praise the Lord, all ye Gentiles; and laud him, all ye people.

Again, Paul is citing from the law of the prophets and speaking of the Gentiles praising the Lord along with his people.

Psalm 117:1 O praise the LORD, all ye nations: praise him, all ye people.

Romans15:12 And again, Esaias saith, There shall be a root of Jesse, and he that shall rise to reign over the Gentiles; in him shall the Gentiles trust.

Isaiah 11:10 And in that day there shall be a root of Jesse, which shall stand for an ensign of the people; to it shall the Gentiles seek: and his rest shall be glorious.

Psalm 22:28 For the kingdom is the LORD's: and he is the governor among the nations.

Isaiah 49:6 And he said, It is a light thing that thou shouldest be my servant to raise up the tribes of Jacob, and to restore the preserved of Israel: I will also give thee for a light to the Gentiles, that thou mayest be my salvation unto the end of the earth.

Micah 4:1 But in the last days it shall come to pass, that the mountain of the house of the LORD shall be established in the top of the mountains, and it shall be exalted above the hills; and people shall flow unto it.

4:2 And many nations shall come, and say, Come, and let us go up to the mountain of the LORD, and to the house of the God of Jacob; and he will teach us of his ways, and we will walk in his paths: for the law shall go forth of Zion, and the word of the LORD from Jerusalem.

4:3 And he shall judge among many people, and rebuke strong nations afar off; and they shall beat their swords into plowshares, and their spears into pruninghooks: nation shall not lift up a sword against nation, neither shall they learn war any more.

All of these verses speak of the Gentile nations in the coming Davidic kingdom on earth. Christ will rule and reign over the nations and the Gentiles will learn of God from Jerusalem. The remnant, the Israel of God, will reign in the kingdom with Christ for a thousand years as kings and priests (Revelation 5:10 Revelation 20:4) and the Gentiles will be blessed through Israel (Isaiah 60:1-3 Genesis 18:18).