# A hyperbolic sum

Calculus Level 5

$\large \sum_{n=1}^\infty \dfrac{\coth(\pi n) }{n^3} = \dfrac{A\pi^B}C$

The equation above holds true for positive integers $$A,B$$ and $$C$$ with $$A,C$$ coprime. Find $$A+B+C$$.

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