$6$ is divisible by $6$.

$6\times6$ is divisible by $6+6$.

$6\times6\times6$ is divisible by $6+6+6$.

Is it true that $\underbrace{6\times6\times\cdots\times6}_{n\text{ times}}$ is divisible by $\underbrace{6+6+\cdots+6}_{n\text{ times}}$ for all positive integers $n$?

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