Simplify $\sum_{i=1}^{n}\sum_{j=i+1}^{n} (i+j)$ $$\sum_{i=1}^n \sum_{j=i+1}^n (i+j)$$
I'm pretty sure it's somewhat simple to solve but I can't get it done.
I know that the given sum is equal to $\frac{n}{2} (n^2-1)$.
I've been on this for 3h+ now and I'm really hoping someone can give me a hint :)

Here is to help you to start:
\begin{align}
\sum_{i=1}^n \sum_{j=i+1}^n (i+j) &= \left( \sum_{i=1}^n \sum_{j=i+1}^n i\right)+\left( \sum_{i=1}^n \sum_{j=i+1}^n j\right) \\
&= \left( \sum_{i=1}^n i (n-(i+1)+1)\right)+\left( \sum_{i=1}^n \left(\sum_{j=1}^n j -\sum_{j=1}^i j \right)\right) \\
\end{align}
Try to simplify it. Formulas to evaluate $\sum i^2$ is useful as well.
