Geometry Riddle: Try and Solve

Question

The combined volume of two cubes with integer side lengths are numerically equal to the combined lengths of their edges. What are the dimensions of the cube?

Answer 1

a and b represents the lengths of the edges

a³ + b³ = 12a + 12b

a³ + b³ = 12(a + b)

a² - ab + b² = 12

a² - ab + b² - 12 = 0

a = (-b ± √(b²- 4(1)(b² - 12)) / 2

Discriminant is -3b² + 48 and must be a perfect square to produce integer values.

What value of b does that?

Answer 2