The Greek doesn't have the word men after "draw all" in the verse, so let's not put it there like many translations assume to do.
Let's leave God's word as it is written. The scripture plainly says, "...will draw all unto Me."
All. What does that mean? Well, it means all. However, a later scripture on this subject does limit it to things on earth and things in heaven, specifically restricting it so that it does not include things beneath, ie Satan and hell.
He drew all to Himself when He was lifted up off the earth on that cross, while He was nailed to that cross. John records a further explanation in John 3:14 where it says, "And as Moses lifted up the serpent, even so the Son of Man must be lifted up." See Psalm 22:16-18 for prophecy about the nailing at the cross.

Witnesses to the idea of Christ bearing the curse at that cross:
Galatians 3:13 Christ has redeemed us from the curse of the law, being made a curse for us:
for it is written, Cursed is everyone that hangeth upon a tree. (ref Deut 21:22,23 )

1st Peter 2:24 "...bore our sins in His own body on the tree (ie wooden cross) that we, being dead to sins should live in righteousness: by whose stripes ye were healed.

1st John 2:2 And He is the propititation for our sins,and not for ours only, but also for the whole world. Romans 8:22 shows us the whole creation is waiting for the manifestion of the salvation of God....

2nd Corinthians 5:14 states clearly that if one died for all then were all dead. Add that together with Him saying He would draw all men to Him at the cross, and you begin to get the complete set of pieces of the picture. Namely, that He drew all unto Himself at that wood cross where He was nailed. All,... includes all men, all sin, all creation that was under the curse, all things....!