Peter's arithmetic

Peter has recently been fascinated by numbers that can be expressed in the form f(a,b,c)=a(bc)3+b(ca)3+c(ab)3 f(a, b, c) = a(b-c)^3+b(c-a)^3+c(a-b)^3 for some integers a,ba,b and cc. He thinks that we should use this system to do arithmetic in future.

How many positive integers N1000 N \leq 1000 can be expressed in the form of f(a,b,c) f(a, b, c) ?

Details and assumptions

As a specific example, since f(1,2,3)=48 f(-1, 2, 3) = 48, hence 4848 can be expressed in the form of f(a,b,c) f(a, b, c) .

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