The sums of powers, \( \sum_{k=1}^{n} k^a \), can be computed more efficiently if we have a closed formula for them.
Sum of powers for a = 1, 2, 3 $$ \sum_{k=1}^{n} k = \frac{n(n+1)}{2} $$
One [intuitive] derivation is presented at brilliant.org :
$$ S_n = 1 + 2 + 3 + … + n $$
… can be reordered as:
$$ S_n = n + (n-1) + (n-2) + … + 1 $$...