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

- $a$ and $b$ are positive integers less than 1,000,
- $a^3-b^3$ is perfect square number,
- $a^3-b^3-3ab=1.$

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

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