Euler sums and Stirling sums

In this paper, using the Bell polynomials and the methods of generating function and integration, we establish various mixed Euler sums and Stirling sums, and present a unified approach to determining the evaluations of unknown Euler sums. As a result, we give the values of two Euler sums of weight 6, six sums of weight 7, twelve sums of weight 8, and twenty sums of weight 9. Thus, all the Euler sums of weights {6,7,9} can be reduced to zeta values, and all the Euler sums of weight 8 can be reduced to linear sum S2,6 and zeta values.