Problem $4$

Use induction to prove that the algorithm to compute the sum of the cubes of the first $n$ positive integers $($shown below$)$ returns the correct value for every positive integer input.

SumCube $(n)$

Input: A positive integer $n.$

Output: $1^3+2^3+$dots$+n^3.$

If $(n=1),$ Return$(1)$

$s$:$\frac{?}{S}=um$ Cube$\frac{n-1}{\frac{?}{?}}$ The recursive call

Return $(n^3+s)$