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.