The single clearest declaration of the existence of God as Father, Son and Holy Spirit — i.e, to use the traditional theological term, as a Trinity — is found in I John 5, which states, in relevant part:
Whoever believes that Jesus is the Christ is born of God. Whoever loves the Father also loves the child who is born of him. By this we know that we love the children of God, when we love God and keep his commandments. For this is the love of God, that we keep his commandments. His commandments are not grievous. For whatever is born of God overcomes the world. This is the victory that has overcome the world: your faith. Who is he who overcomes the world, but he who believes that Jesus is the Son of God? This is he who came by water and blood, Jesus Christ; not with the water only, but with the water and the blood. It is the Spirit who testifies, because the Spirit is the truth. For there are three who testify in heaven: the Father, the Word, and the Holy Spirit; and these three are one. And there are three that testify on earth: the Spirit, the water, and the blood; and the three agree as one. If we receive the witness of men, the witness of God is greater; for this is God’s testimony which he has testified concerning his Son. He who believes in the Son of God has the testimony in himself. He who doesn’t believe God has made him a liar, because he has not believed in the testimony that God has given concerning his Son. The testimony is this, that God gave to us eternal life, and this life is in his Son. He who has the Son has the life. He who doesn’t have God’s Son doesn’t have the life… We know that the Son of God has come, and has given us an understanding, that we know him who is true, and we are in him who is true, in his Son Jesus Christ. This is the true God, and eternal life.
I John 5:1-12, 20