One more of those

read about dirichlet convolution (still under construction, if you want to help DM me at slack)

the defination of dirchlet series $DG(F;s)=\sum_{n=1}^\infty \dfrac{F(n)}{n^s}$ where F is an arithmetic function. we are to know $DG(f*g;s)=D(f;s)D(g;s)$ where $f*g$ denotes the dirichlet convolution of f and g. define function $f(n)=n^2$ and $u(n)=1$ . so we see that $f*u=\sum_{d|n}\left(f(d)u\left(\dfrac{n}{d}\right)\right)$ but u of anything is one so: $f*u=\sum_{d|n}\left(d^2\right)=\sigma_2(n)$ so $DG(\sigma_2;6)=DG(f;6)DG(u;6)=\left(\sum_{n=1}^\infty \dfrac{n^2}{n^6}\right)\left(\sum_{n=1}^\infty \dfrac{1}{n^6}\right)=\zeta(4)\zeta(6)$ we know we can calculate zeta of even integers using Bernoulli numbers.so, this equals after simplification $\dfrac{\pi^{10}}{\boxed{85050}}$