# Inspired by me

Calculus Level 5

Let $$\displaystyle { H }_{ n }^{ (3) }=\sum _{ k=1 }^{ n }{ \frac { 1 }{ { k }^{ 3 } } }$$. If $\sum _{ n=1 }^{ \infty }{ \frac { { H }_{ n }^{ (3) } }{ n^{ 2 } } }$

is in the form $\dfrac { a\zeta (b) }{ c } -\dfrac { \pi ^{ d }\zeta (f) }{ g }$

for positive integers $$a,b,c,d,f$$ and $$g$$ where $$a$$ and $$c$$ are coprime, find $$a+b+c+d+f+g$$.

Notation: $$\zeta(\cdot)$$ denotes the Riemann zeta function.

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