Sum formulas of mltiple zeta values with arguments are multiple of a positive integer

For $k\le n$, let $E(mn,k)$ be the sum of all multiple zeta values of depth $k$ and weight $mn$ with arguments are multiples of $m\ge 2$. More precisely, $E(mn,k)=\sum_{|\boldsymbol{\alpha}|=n}\zeta(m\alpha_1,m\alpha_2,\ldots, m\alpha_k)$\mathrm{.}Inthispaper,wedevelopaformulatoexpress$E(mn,k)$ in terms of $\zeta (\{m{\}}^p)$ and ${\zeta }^{\star }(\{m{\}}^q)$, $0\le p,q\le n$. In particular, we settle Gen\v{c}ev’s conjecture on the evaluation of $E(4n,k)$ and also evaluate $E(mn,k)$ explicitly for small even $m\le 8$.