Tornheim type series and nonlinear Euler sums

In this paper, we develop an approach to evaluation of non-linear Euler sums. The approach is based on Tornheim type series computations. By the approach, we can obtain some closed form representations of quadratic and cubic sums in terms of zeta values and linear sums. Furthermore, we also evaluate several other series involving harmonic numbers. Some interesting new consequences and illustrative examples are considered. (C) 2016 Elsevier Inc. All rights reserved.