# Divisibility!

$P=(a^{3} -b^{3})(b^{3} -c^{3})(c^{3} -d^{3})(d^{3} -a^{3})(c^{3} -a^{3})(d^{3} -b^{3})$

If $$a$$, $$b$$, $$c$$, and $$d$$ are four positive integers then $$P$$ is always divisible by a square integer.

Find the maximum value of this integer.

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