Many squares

We can get squares from side equal to 1 to side equal to n. It is possible to learn that for squares with side n + 1 - k, where $1 \leq k \leq n$ , we can build $k^{2}$ squares. Let's N to be the total number of squares we can build, then $N = \sum_{i = 1}^n i^{2} = \frac{n\times(n + 1)\times(2n + 1)}{6} = 1240$ . The solution for this equation is n = 15. Therefore $\boxed{n + n^{2} = 15 + 15^{2} = 240}$

Paul already said it all. I just wanted to add that we can solve the equation fully or use the shortcut of
n = floor[ (3 × {total squares} )⅓ ]