Find $n$ for a $\sum_{x=1}^n \left[(x+1)^3-x^3\right]$ $$ \sum_{x=1}^n \left[(x+1)^3-x^3\right]$$
This is my sum, I tried simplfifying and got $3x^2+3x+1$ but Im stuck on how to resolve the sum for $n$.

Note that
$$\sum_{x=1}^n \left[(x+1)^3-x^3\right] =\color{red}{2^3}-1^2+\color{red}{3^3}-\color{red}{2^3}+\ldots+\color{red}{n^3}-\color{red}{(n-1)^3}+(n+1)^3-\color{red}{n^3}$$
