Is there a closed form for this sum?
$$\sum _{n=1}^{\infty }\frac{\coth (xn)}{n^3}$$
I have tried using
$$x\coth \left(xn\right)=\frac{1}{n}+2n\sum _{k=1}^{\infty }\frac{1}{n^2+\left(\frac{\pi }{x}\right)^2k^2}$$
To solve but got stuck at evaluating
$$\sum _{n=1}^{ \infty}\sum _{k=1}^{\infty }\frac{1}{k^2\left(n^2+\left(\frac{\pi }{x}\right)^2k^2\right)}$$