(In reply to computer solution
"Part B: Any solution for this part must have a sum of 2 positive cubes and a difference of 2 positive cubes (same as adding a negative cube) equaling the same value. "
This is not the case as, for example, 9^3 - 2^3 = 16^3 - 15^3 = 721. Also, for 728, there's a third way besides the two you list, and that's 12^3 - 10^3, and thus a second difference of cubes for this number.
Posted by Charlie
on 2010-08-02 16:08:54