I see an equation, "a^3+a^2b+ab^2-ba^2-b^2a-b^3=a^3-b^3", and both sides of the equation factor to the same term, "(a-b)(a^2 + ab + b^2)".  Hence, any value for 'a' or for 'b' will result in an infinite number of solutions. 

As an equation, the inquiry is ambiguous.  Factoring each side of the equation is a useful approach.