69th Belarusian Mathematical Olympiad

Find all possible values of digits $a$ and $b$ such that $$(ab{)}^3=\overline{(a-3)(b-3)(b+2)(a+2)ab}.$$ (As usual, by $\overline{xyz}$ we denote an integer number, which decimal representation consists of digits $x,y,\dots ,z$ in that order.)