8 cubes are used to build a 2 by 2 Cube. How many cubes needed to build a cube that has three cubes along each edge?

The number cubes needed when we have three cubes along each edge is 27 cubes

Step-by-step explanation:

The given parameters for the building of a cubic prism are;

The number of cubes used to build the 2 by 2 cube = 8 cubes

Let 'x' represent the length of each cube, we have;

The volume of a 2 by 2 cube = 2·x × 2·x × 2·x = 8·x³

Where x³ represents the volume of each cube

When we have three cubes along each edge, the total volume, becomes;

V = 3·x × 3·x × 3·x = 27·x³

The number cubes needed when we have three cubes along each edge, n = (The total volume of the cubes)/(The volume of each cube)

∴ The number cubes needed when we have three cubes along each edge, n = 27·x³/(x³/cube) = 27 cubes.