Prove that $\sum_{i=1}^k i!$ can never be of the form $n^m$ (where $n,m\in\mathbb N$ and $m\ge 2$) for $k\ge 4$.

Question

I have proved that for $k\ge 4$ the sum $$\sum_{i=1}^k i!$$ can never be a perfect square i.e., of the form $n^2\, (m=2).$ But am struggling with the generalisation i.e., with the form $n^m$. Is the statement valid? I found this question on quora and no one has answered it.. Please suggest something... Thanks in advance.