Find a four digit number $mcdu$ ,such that $m+c+d+u=(c-d)^3$

Question

Find a four digit number $mcdu$, such that $m+c+d+u=(c-d)^3$

None of the digits are 0.

I tried algebraic method, no success.

Answer 1

Hint:

Having in mind that the LHS is the sum of four digits, what are the possible values of $(c-d)^3$?