On two conjectural series involving Riemann zeta function

Riemann zeta function is important in a lot of branches of number theory. With the help of the operator method and several transformation formulas for hypergeometric series, we prove four series involving Riemann zeta function. Two of them are series expansions for $\zeta(7)$ and $\zeta(3)^2$ recently conjectured by Z.-W. Sun.