I'm looking for a closed form for the expression 
$$
\sum\_{k=1}^{\infty}\frac{1}{(2k)^5-(2k)^3}
$$
I know that Ramanujan gave the following closed form for a similar expression
$$
\sum\_{k=1}^{\infty}\frac{1}{(2k)^3-2k}= \ln(2)-\frac{1}{2}
$$
I wonder if it is possible to find such a similarly simple and nice closed form for the above case. 


Thanks.



Finding a closed form for $\sum_{k=1}^{\infty}\frac{1}{(2k)^5-(2k)^3}$
$$  \frac{1}{(2k)^5 - (2k)^3} + \frac{1}{(2k)^3} = \frac{1 + (2k)^2 - 1}{(2k)^5 - (2k)^3} = \frac{1}{(2k)^3 -2k}$$


So by Ramanujan's result:


$$\sum\_{k=1}^{\infty} \frac{1}{(2k)^5 - (2k)^3} = \ln(2) - \frac{1}{2} - \frac{1}{8}\zeta(3)$$


