Geometry

Question Analysis
This question involves the concept of similar cubes, focusing on the relationship between the volumes of similar solids.
The main focus is understanding that for similar cubes, the ratio of volumes is equal to the cube of the ratio of their edge lengths.

Key Concept Explanation
For two similar solids, when the scale factor (ratio of corresponding linear dimensions) is , the ratio of their volumes .
In the case of cubes, since all edge lengths are equal, the edge - length ratio directly determines the volume ratio.

Step-by-Step Solution
Let the edge - length ratio of the two cubes be , and the volume of the smaller cube cubic centimeter, and the volume of the larger cube be .
We know that