What is the volume of a cube given its side length?

The volume of a cube is determined by the formula that involves cubing the length of one of its sides. Since all sides of a cube are equal, the volume can be calculated as the side length multiplied by itself three times. Thus, if the side length of the cube is represented as "side," the formula for the volume becomes side × side × side, or side³.

This formulation captures how three-dimensional space is occupied by the shape. When you think about it, this can be visualized as filling the cube with unit cubes, where the number of unit cubes that fit along each dimension (length, width, and height) is equal to the side length. Therefore, multiplying the side length three times accounts for the three dimensions of the cube, yielding the total volume as side³.

It's vital to note that the other options either misrepresent the volume calculations or do not apply to a three-dimensional object like a cube. The correct understanding of geometric properties, especially when dealing with volume, supports accurate calculations and applications in mathematical contexts.