Explanation:
x^3 = volume of smaller cube
(x+2)^3 = volume of larger
(x+2)^3 - x^3 = 152 cm^3 <=======given Expand
x^3 + 6x^2 + 12x + 8 - x^3 = 152 simplify
6x^2 + 12x - 144 = 0
6 ( x^2 + 2x - 24) = 0 factor
6 ( x+6)(x-4) = 0 shows x = 4
the smaller cube is 4 x 4 x 4 cm ( length = 4cm)