Question 3
Suppose $a,b,c,d,e$ are consecutive positive integers with $a\lt b\lt c\lt d\lt e$. The sum $b+c+d$ is a perfect square and $a+b+c+d+e$ is a perfect cube. Find the smallest value of $c$.
Enter the exact number only; fractions are allowed.
Enter the exact number only; fractions are allowed.