I made a post covering some of "John 6" some time back:
[quoting that entire post (some things might not transfer correctly, the emphasis, etc)]
[note, this post will cover the following passages: Acts 3:22-26; Matthew 10:5-7; John 12:32-33; John 6:41-58 [64][35]; John 7:17; John 17:6-20; 1 John 4:14; 1 John 5:10-12; along with my comments]
Acts 3 [blb]-
22 For Moses said, ‘The Lord your God will raise up to you [this is His earthly ministry BEFORE His death] a prophet like me out from your brothers. You will listen to Him in all things, as many as He might say to you. 23 And it will be that every soul who might not heed that prophet will be utterly destroyed out from the people.’
24 And also all the prophets from Samuel, and those subsequently, as many as have spoken, also have proclaimed these days. 25 You are the sons of the prophets and of the covenant that God made with your fathers, saying to Abraham, ‘And in your seed all the families of the earth will be blessed.’ 26 God, having raised up His servant [that is, in His earthly ministry BEFORE His death], sent Him first to you, blessing you in turning away each of you from your wickednesses.”
[and verse 19 had said, "Repent ye therefore, and be converted, that your sins may be blotted out, when the times of refreshing shall come from the presence of the Lord; And He shall send Jesus Christ... Whom..." etc]
[Matt10:5-7 had said, "5 These twelve, Jesus sent forth, having instructed them, saying: “Do not go into the way of the Gentiles and do not enter into any city of the Samaritans. 6 But go rather to those being the lost sheep of the house of Israel. 7 And going on, proclaim, saying, ‘The kingdom of the heavens has drawn near!’ (this is not what is to be proclaimed presently [in "this present age [singular]"], but will again in the future trib, in slightly differing phrasing) ]
John 12:32-33 [blb] -
32 And I, if I am lifted up from the earth, will draw all to Myself.” 33 Now He was saying this, signifying by what death He was about to die. [compare this with your John 6:44 verse]
John 6:41-58 [blb] - [dialogue with skeptical inquiring multitude (vv.24-29), that though they'd seen Him, still did not believe (v.36) ]
41 Therefore the Jews were grumbling about Him because He said, “I am the bread having come down from heaven.” 42 And they were saying, “Is this not Jesus the son of Joseph, whose father and mother we know? How then does He say, ‘I have come down from heaven?’”
43 Jesus answered and said to them, “Do not grumble with one another. 44 No one is able to come to Me unless the Father, the one having sent Me, draws him, and I will raise him up in the last day. 45 It is written in the prophets: ‘And they will all be taught of God.’ Everyone having heard from the Father and having learned, comes to Me. 46 Not that anyone has seen the Father, except the One being from God; He has seen the Father.
47 Truly, truly, I say to you, the one believing has eternal life. 48 I am the bread of life. 49 Your fathers ate the manna in the wilderness and died. 50 This is the bread coming down from heaven, that anyone may eat of it and not die. 51 I am the living bread, having come down from heaven. If anyone shall have eaten of this bread, he will live to the age. And also, the bread that I will give for the life of the world is My flesh.”
52 Therefore the Jews were arguing with one another, saying, “How is this man able to give us His flesh to eat?”
53 Therefore Jesus said to them, “Truly, truly, I say to you, unless you shall have eaten the flesh of the Son of Man, and shall have drunk His blood, you do not have life in yourselves. 54 The one eating My flesh and drinking My blood has eternal life, and I will raise him up in the last day. 55 For My flesh is true food, and My blood is true drink.
56 The one eating My flesh and drinking My blood abides in Me, and I in him. 57 As the living Father sent Me and I live because of the Father, so also the one feeding on Me, he also will live because of Me. 58 This is the bread having come down from heaven, not as the fathers ate and died. The one eating this bread will live to the age.”
[the key issue all through is: faith or lack of faith - Jn6:29, 35, 40, 47, 64, and He symbolizes faith as appropriating/eating/drinking Himself - Jn6:35, 51, 53, 58; and then in JOHN 7:17 He emphasized the human response factor: "17 If anyone desires to do His will, he will know concerning the teaching, whether it is from God, or I speak from Myself."]
John 17:6-20 [blb] -
Prayer for the Disciples
6 I revealed Your name to the men whom You have given Me out of the world. [<--He did this personally] They were Yours, and to Me You gave them, and they have kept Your word. 7 Now they have known that all things You have given Me are of You. 8 For the words that You have given Me I have given them, and they received them, and knew truly that I came forth from You; and they believed that You sent Me.
9 I am praying concerning them. I do not pray concerning the world, but concerning those whom You have given Me, for they are Yours. 10 And all things of mine are Yours, and Yours Mine. And I have been glorified in them. 11 And I am no longer in the world, and yet they are themselves in the world, and I am coming to You.
Holy Father, keep them in Your name, which You have given Me, that they may be one as we are. 12 When I was with them, I was keeping them in Your name, which You have given Me. And I guarded them, and none of them has perished, except the son of destruction, that the Scripture might be fulfilled.
13 But now I am coming to You, and I speak these things in the world, so that they may have My joy fulfilled within them. 14 I have given them Your word, and the world hated them, because they are not of the world, even as I am not of the world.
15 I do not ask that You should take them out of the world, but that You should keep them from evil. 16 They are not of the world, as I am not of the world. 17 Sanctify them by the truth; Your word is truth. 18 As You sent Me into the world, I also sent them into the world; 19 and for them I sanctify Myself, that they also may be sanctified in truth.
Prayer for all Believers
20 But I do not ask for these only, but also for those believing in Me through their word, [...]
[so this is showing the distinction between "they have kept your word" / He had [aorist] shown the Father to them, personally (that is, to living disciples the Father had given Him, especially the Apostles), AND "those believing IN ME through their word"--Recall 1Jn4 "14 And we have seen and testify that the Father has sent the Son as Savior of the world." And 1Jn5, "10 The one believing in the Son of God has the testimony in himself; the one not believing God has made Him a liar, because he has not believed in the testimony that God has testified concerning His Son. 11 And this is the testimony: that God has given to us eternal life, and this life is in His Son. 12 The one having the Son has life; the one not having the Son of God does not have life."]
[end of quoting that post]