Square And Cubes Challenging You

Find the sum of all possible solutions of a2b2a^2-b^2 for the following conditions:

  • aa and bb are positive integers less than 1,000,
  • a3b3a^3-b^3 is perfect square number,
  • a3b33ab=1.a^3-b^3-3ab=1.

Example: If possible solutions of (a,b)(a,b) are (2,1)(2,1) and (3,2)(3,2) then the sum of all (a2b2)=(41)+(94)=8(a^2-b^2)=(4-1)+(9-4)=8.

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