# Two Math Professors

**Number Theory**Level 4

Prof. Uno say, "It just crossed my mind that when we first met, the square of your age contains the same three digits as the square of my age but in a different order."

Prof. Dos reply, "If you take the square of the sum of our ages when we first met and split it into two 2-digit numbers, you will have my age then and your age now."

If the sum of their current ages can be expressed as a 3-digit number \(\overline{abc}\), then calculate \(a^3+b^3+c^3\).