sequences and series - How do i evaluate this sum :$sum _{m=1}^{infty } sum _{k=1}^{infty } frac{m(-1)^m(-1)^klog(m+k)}{(m+k)^3}$?

How do I evaluate the following sum:

$$\sum _{m=1}^{\infty } \sum _{k=1}^{\infty } \frac{m(-1)^m(-1)^k\log(m+k)}{(m+k)^3}$$

Note I used many idea such as :Hochino's Idea and taylor expansion of

$\log(1+x)$ at $x=1$ where $x=\frac{k}{m}$ ,but those methods not work .

and also i tried to write $\log(m+k)$ as a power series but it became to me as a

triple series then it is very complicated for evaluation !!!

Thank you for any help