John 6:35: "Jesus said to them, 'I am the bread of life; whoever comes to me shall not hunger, and whoever believes in me shall never thirst.'"
1 Corinthians 11:23-26: "23 For I received from the Lord what I also delivered to you, that the Lord Jesus on the night when he was betrayed took bread, 24 and when he had given thanks, he broke it, and said, 'This is my body which is for you. Do this in remembrance of me.' 25 In the same way also he took the cup, after supper, saying, 'This cup is the new covenant in my blood. Do this, as often as you drink it, in remembrance of me.' 26 For as often as you eat this bread and drink the cup, you proclaim the Lord's death until he comes."
John 6:48-58: "48 'I am the bread of life. 49 Your fathers ate the manna in the wilderness, and they died. 50 This is the bread that comes down from heaven, so that one may eat of it and not die. 51 I am the living bread that came down from heaven. If anyone eats of this bread, he will live forever. And the bread that I will give for the life of the world is my flesh.'
"52 The Jews then disputed among themselves, saying, 'How can this man give us his flesh to eat?' 53 So Jesus said to them, 'Truly, truly, I say to you, unless you eat the flesh of the Son of Man and drink his blood, you have no life in you. 54 Whoever feeds on my flesh and drinks my blood has eternal life, and I will raise him up on the last day. 55 For my flesh is true food, and my blood is true drink. 56 Whoever feeds on my flesh and drinks my blood abides in me, and I in him. 57 As the living Father sent me, and I live because of the Father, so whoever feeds on me, he also will live because of me. 58 This is the bread that came down from heaven, not like the bread the fathers ate and died. Whoever feeds on this bread will live forever.'"
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Part of the refrain ("Eat this bread, drink this cup") comes from the passage from 1 Corinthians 11, and part ("Come to Him and never be hungry... Trust in Him and you will not thirst") from John 6:35.
The first two verses also come from the passage from 1 Corinthians 11. The second verse ("As often as you eat this bread and drink this cup, you show His death until He comes again") is just a paraphrase of verse 26.
The third through fifth verses come from John 6:48-58: the third and fifth verses from verse 54 and the fourth verse from either verse 51 or 58.