The main goal of this paper is the presentation of an elementary analytic technique which enables the evaluation of the so-called restricted sum formulas involving multiple zeta values with even arguments, i.e. $$E(2c,K):=\sum_{\substack{\sum_{j=1}^{K}c_{j}=c\\{c}_{j}\in\mathbb{N}}} \zeta(2c_1,\ldots ,2c_K),$$ where c and K are arbitrary positive integers with \({c\ge K}\). Though the young and general theory of the multiple Riemann zeta function with a rich application potential may be rather complicated, our contribution makes the evaluation of the term E(2c,K) intelligible to a broad mathematical audience.