Asymptotic calculation check for triple-nested for-loops
As Yuval Filmus and gnasher729 have pointed out my original equation for the repetition structure is indeed wrong. I believe this to be the true correct answer:

$\sum_{i=1}^{n} (\sum_{j=1}^{i^2} j)$

$= \sum_{i=1}^{n} (\frac{i^4+i^2}{2})$

$= \frac{1}{2} \sum_{i=1}^{n}i^4 + \frac{1}{2} \sum_{i=1}^{n}i^2$

$\approx \frac{n^5}{10} + \frac{n^3}{6}$

$\therefore runtime \in O(n^5)$