This Bible contradiction is from the Skeptic's Annotated Bible.

Verses

Jesus carried his own cross.

John 19:17 View context

And he bearing his cross went forth into a place called [the place] of a skull, which is called in the Hebrew Golgotha:

Simon the Cyrenian carried Jesus' cross.

Matthew 27:32 View context

And as they came out, they found a man of Cyrene, Simon by name: him they compelled to bear his cross.

Mark 15:21 View context

And they compel one Simon a Cyrenian, who passed by, coming out of the country, the father of Alexander and Rufus, to bear his cross.

Luke 23:26 View context

And as they led him away, they laid hold upon one Simon, a Cyrenian, coming out of the country, and on him they laid the cross, that he might bear [it] after Jesus.