The problem asks for the volume of a cube with sides of 3 cm each.

To find the volume $V$ of a cube, the formula is:

$V = s^3$

Where $s$ is the length of one side of the cube. In this case, $s = 3$ cm:

$V = 3^3 = 3 \times 3 \times 3 = 27 \, \text{cm}^3$

Thus, the correct answer is:

$\boxed{27 \, \text{cm}^3}$

Would you like a more detailed explanation or any further clarifications?

Here are 5 additional questions related to this concept:

1. What is the surface area of a cube with sides of 3 cm?
2. If the side of the cube is doubled, how does the volume change?
3. What would be the volume of a cube with sides of 4 cm?
4. How does the formula for the volume of a cube compare to the formula for the volume of a rectangular prism?
5. How is the unit for volume (cubic centimeters) different from the unit for area (square centimeters)?

Tip: When working with cubes, remember that the volume scales with the cube of the side length, meaning small changes in side length result in large changes in volume.