  In this paper, we obtain a sharp upper bound for the sum of the first $k$-th
eigenvalues for this Dirichlet problem of poly-Laplacian with any order, which
is viewed as an extension of the result due to Cheng and Wei (Journal of
Differential Equations, 255 (2013), 220-233). In particular, if $l=2$ and $k$
is large enough, we give an important improvement of their result.
