# Inverse Sum Cubed

Calculus Level 4

$\large\displaystyle\sum_{n=1}^{\infty} \left({\displaystyle\sum_{k=0}^nk^3} \right)^{-1}$

If the value of the series above can be expressed as $$\dfrac{a\pi^2}b-c$$ where $$a,b,c$$ are positive integers, and $$a,b$$ are coprime to each other, find the value of $$a+b+c$$.

See Also Inverse Sum and Inverse Sum Squared.

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