Two mathematicians meet at their school reunion.
A: Hey old friend, I heard you have 5 children. How old are they?
B: The sum of their ages is a cube number,
A: But, I still don't know their ages.
B: The product of their ages is a cube number too.
A: OK, I know now.
Find the most reasonable answer. How old are B's children?
Note, with most reasonable it is meant that you must look for an answer such that:
The age of the children is a positive integer number.
The children all have a unique age.
Of all valid possibilities, the one where the oldest child is as young as possible.