  Many $\mathbb{Q}$-linear relations exist between multiple zeta values, the
most interesting of which are various weighted sum formulas. In this paper, we
generalized these to Euler sums and some other variants of multiple zeta values
by considering the generating functions of the Euler sums. Through this
approach we are able to re-prove a few known formulas, confirm a conjecture of
Kaneko and Tsumura on triple $T$-values, and discover many new identities.
