Let $G$ be a finite group and $g$ be a commutator.
It can be shown that if $m$ is a positive integer coprime to order of $g$, then $g^m$ is also a commutator (link).
Q. Is there any example of a finite group such that $g$ is a commutator but for $m$ a divisor of order of $g$, the element $g^m$ is not a commutator?