The volume $V$ of a cube is calculated using the formula:

$V = s^3$

where $s$ is the length of one side of the cube. Given that the side length $s = 32 \, \text{cm}$, the volume of the cube is:

$V = 32^3 = 32 \times 32 \times 32 = 32,768 \, \text{cm}^3$

So, the volume of the cube is 32,768 cubic centimeters.

Would you like more details on how this formula works, or have any other questions?

Here are some related questions for further exploration:

1. How do you calculate the surface area of a cube?
2. What would happen to the volume of a cube if its side length is doubled?
3. Can the volume of a cube be negative or zero?
4. How do you calculate the volume of a rectangular prism, and how is it different from a cube?
5. What are some real-world applications of calculating the volume of a cube?

Tip: To avoid errors in cubic calculations, remember that multiplying the side length three times is essential, as it's different from just squaring the side.