Notice that in answering this question Brent took advantage of a key thing.
In questions such as this one that basically state that if you do something with any set of numbers that fit the constraints described in the question you will always get the same result, it is safe to plug in any numbers that fit the constraints of the question.
In this case, the implication of the question is that in tripling the lengths of the sides of the cube you will always get a larger cube the volume of which is a particular multiple of the volume of the smaller cube.
Since no matter what the numbers are, as long as the greater length is triple the shorter length, you will always get the same result, then you can select any numbers that fit that constraint.
This principle can be applied to answering many different types of GMAT questions, sometimes making questions that seem insanely challenging rather easy to answer.
