  In this paper we prove some new identities for multiple zeta values and
multiple zeta star values of arbitrary depth by using the methods of integral
computations of logarithm function and iterated integral representations of
series. By applying these formulas, we can prove that multiple zeta star values
whose indices are the sequences $(\bar 1,\{1\}_m,\bar 1)$ and $(2,\{1\}_m,\bar
1)$ can be expressed polynomially in terms of zeta values, polylogarithms and
$\ln2$. Finally, we also evaluate several restricted sum formulas involving
multiple zeta values.
