That's a circular question, since you already labeled it a triple.
If what you're saying is the guy was at 3d when the cut was fumbled, the scorekeeper has to make a judgment call. If the runner had stopped but started again after the ball got bobbled, then it would be triple + scored on error. If the runner never slowed down, typically you don't presume that the out could have been made on the relay, so it is impossible to say the bobble caused an additional advance. In that case, HR.
Also, below the age of 12, it's a homer all the way!