Let $G$ be a group where $(ab)^3=a^3b^3$ . Prove that $\{ x^3 \mid x \in G \}$ is a normal subgroup of $G$.
Let $(G,•)$ be a group in which $(a•b)^3 = a^3•b^3$. Prove that $H=\{x^3 : x \in G\}$ is a normal subgroup of $G$.