A cube of side `4` `cm` contains a sphere touching its side. Find the volume of the gap in between.

Explanation

To find the volume of the gap between a cube and a sphere that touches its sides, we can follow these steps:

### Step 1: Identify the side length of the cube
The side length of the cube is given as \(4 \, \text{cm}\).

### Step 2: Find the radius of the sphere
Since the sphere touches the sides of the cube, the diameter of the sphere is equal to the side length of the cube. Therefore, the radius \(r\) of the sphere is half of the side length:
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