Problem $3.(30$ points$)$

Consider the following recursive algorithm for computing the sum of the first n cubes: S$($n$)=13+23+...+$ n$3$

ALGORITHM S $($n$)$

$//$Input: A positive integer n

$//$Output: The sum of the first n cubes if n $=1$ return $1$

else return S$($n $1)+$ n $$ n $$ n

Set up and solve a recurrence relation for the number of times the algorithm$$s basic operation is executed.