  We obtain a weighted sum formula of the zeta values at even arguments, and a
weighted sum formula of the multiple zeta values with even arguments and its
zeta-star analogue. The weight coefficients are given by (symmetric)
polynomials of the arguments. These weighted sum formulas for the zeta values
and for the multiple zeta values were conjectured by L. Guo, P. Lei and J.
Zhao.
