  In this paper we present a new family of identities for Euler sums and
integrals of polylogarithms by using the methods of generating function and
integral representations of series. Then we apply it to obtain the closed forms
of all quadratic Euler sums of weight equal to ten. Furthermore, we also
establish some relations between multiple zeta (star) values and nonlinear
Euler sums. As applications of these relations, we give new closed form
representations of several cubic Euler sums through single zeta values and
linear sums. Finally, with the help of numerical computations of Mathematica or
Maple, we evaluate several other Euler sums of weight ten.
