Why $T(n)=6T(n-1) + n^3$ has such a mess solution?

I tried to solve the recurrence relation $$T(n) = 6T(n-1) + n^3$$ using the tree method, and figured out that the root will be $$n^3$$, the second level will be $$6^1(n-1)^3$$, the third will be $$6^2 (n-2)^3$$, and so on.

The formula as I understood it is: $$\sum_{i=0}^n 6^i(n-i)^3$$.

After entering this in Wolfram, the result is:

$$\sum_{i=0}^n 6^i(n-i)^3 = \frac{1}{625}(-125n^3-450n^2-630n+366(6^n-1)).$$

And it doesn’t look like a valid solution. Did I miss anything?