\[P=(a^{3} -b^{3})(b^{3} -c^{3})(c^{3} -d^{3})(d^{3} -a^{3})(c^{3} -a^{3})(d^{3} -b^{3})\]

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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