# Bro , do you even Euler?

\begin{aligned} a^3-b^3-c^3&=&3abc \\ a^2 &=& 2(b+c) \\ \end{aligned}

Find the triplets $(a,b,c) \in \mathbb {Z^{+}}$ that satisfy the system of equations above.

Details and assumptions:

• Input the sum of all possible numbers in the triplets as an answer. As an explicit example, if $(1,2,3)$ is the only triplet, input 6 but if $(2,3,4)$ is also an answer input 15.
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