John 12:28 Father, glorify thy name. Then came there a voice from heaven, saying, I have both glorified it, and will glorify it again. 29 The people therefore, that stood by, and heard it, said that it thundered: others said, An angel spake to him. 30 Jesus answered and said, This voice came not because of me, but for your sakes. 31 Now is the judgment of this world: now shall the prince of this world be cast out. 32 And I, if I be lifted up from the earth, will draw all men unto me. 33 This he said, signifying what death he should die.
Verse 33 is why He had said verse 32.
It is not the same message in regards to the Father because not everyone that saw Him crucified, believed in Him, certainly not the Pharisees that put Him there. ( Granted, Jesus gave up His life; the Jews did not really take it away from Him )
John 10:17 Therefore doth my Father love me, because I lay down my life, that I might take it again. 18 No man taketh it from me, but I lay it down of myself. I have power to lay it down, and I have power to take it again. This commandment have I received of my Father.
So the scripture that singled out the Father by that exception for how men are drawn unto the Son means only the Father did it. Yes, His crucifixion on the cross was the focus as to Who the Father was drawing them to, but still only the Father does this by the use of that word "except" in His words. Indeed, this scripture testify that the Father gives those to be saved to the Son per the father's will.
John 6: 38 For I came down from heaven, not to do mine own will, but the will of him that sent me. 39 And this is the Father's will which hath sent me, that of all which he hath given me I should lose nothing, but should raise it up again at the last day. 40 And this is the will of him that sent me, that every one which seeth the Son, and believeth on him, may have everlasting life: and I will raise him up at the last day.