Suppose that $(ab)^3 = a^3 b^3$ for all $a, b \in G$. Prove that G must be an abelian goup [Group Theory].

Let G be a finite group whose order is not divisible by $3$. Suppose that $(ab)^3 = a^3 b^3$ for all $a, b \in G$. Prove that G must be abelian.

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