What's so special about 2760

Find the number of ordered triples of integers \((a,b,c)\) that satisfy the equation \[a(b-c)^3+b(c-a)^3+c(a-b)^3=2760\]

Details and assumptions

The order matters: \((-8,-5,15)\) and \((15,-8,-5)\) are considered different solutions.

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