The synoptic gospels (that is: Matthew, Mark, and Luke) are agreed that a man called Simon of Cyrene was forced to carry the cross of Jesus up to Golgotha where he was crucified. Here is Mark 15:21:
Matthew 27:32 and Luke 23:26 are nearly identical. On the other hand, this is John 19:17:
Pretty much the only solution is to state that Jesus carried the cross part of the way, and Simon the rest of the way. Yet it's remarkable that the synoptics should say Simon carried it, John should say Jesus carried it, and nobody says they both carried it. More importantly, the natural and honest reading of John is that Jesus carried the cross all the way, especially since the clause "bearing his own cross" is contained in a sentence that covers the entire journey.