If a<b<c<d<e are consecutive positive integers such that b+c+d is a perfect square and a+b+c+d+e is a perfect cube, what is the smallest possible value of c ?
If a<b<c<d<e are consecutive positive integers such that b+c+d is a perfect square and a+b+c+d+e is a perfect cube, what is the smallest possible value of c ?