An equation involving 2760.

Find the number of ordered triples of integers (a,b,c)(a,b,c) that satisfy the equation a(bc)3+b(ca)3+c(ab)3=2760.a(b-c)^3+b(c-a)^3+c(a-b)^3=2760.

Note that the order matters: (8,5,15)(-8,-5,15) and (15,8,5)(15,-8,-5) are considered different solutions.

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