Sum formulas of multiple zeta values with arguments multiples of a common positive integer

For k≤n, let E(m,n,k) be the sum of all multiple zeta values of depth k and weight mn with arguments multiples of m≥2. More precisely, E(m,n,k)=∑|α|=nζ(mα1,mα2,…,mαk). In this paper, we develop a formula to express E(m,n,k) in terms of ζ({m}p) and ζ⋆({m}q), 0≤p,q≤n. In particular, we settle Genčev's conjecture on the evaluation of E(4,n,k) and also evaluate E(m,n,k) explicitly for small even m≤8.