Real Bible Translation

And he who is carrying the Stake to his own self,¹¹⁹ came out into the one who is spoken 'the Place/Position of the Skull' which is spoken in Hebrew, 'Rolling-Skull,'

Julia Smith Literal 1876 Translation:
And they took Jesus, and led away: and bearing his cross he went out into a place called Kranium, which in Hebraic is called Golgotha:

LITV Translation:
And He went out bearing His cross, to the place called Of a Skull (which is called in Hebrew, Golgotha),

ESV Translation:
and he went out, bearing his own cross, to the place called The Place of a Skull, which in Aramaic is called Golgotha.

Footnotes

119

The phrase "βαστάζων ἑαυτῷ" (bastazōn heautō) translates to "bearing to his own self" or "carrying to himself" or with the accusative "the Stake": bearing the stake to his own self.

"βαστάζων" (bastazōn) is the present active participle form of the verb "βαστάζω" (bastazō), which means "to carry" or "to bear."
"ἑαυτῷ" (heautō) is the dative form of the reflexive pronoun "ἑαυτός" (heautós), which means "to his own self."

The whole phrase then, "βαστάζων ἑαυτῷ τὸν σταυρὸν" (bastazōn heautō ton stauro) would be:

"Carrying to his own self the stake."

Because ἑαυτῷ is not genitive, a translation of "carrying his own cross/stake" is therefore, for lack of any better way to put it, a lie. It is not "the Cross of himself" but rather "the Cross to himself."