To solve this problem, we need to use the relationship between the surface area and the volume of a cube.

1. Surface Area of a Cube: The surface area $A$ of a cube with side length $s$ is given by the formula:

$A = 6s^2$

We know the surface area is 96 square centimeters. So, we set up the equation:

$6s^2 = 96$

Solving for $s$:

$s^2 = \frac{96}{6} = 16$

$s = \sqrt{16} = 4 \, \text{cm}$

2. Volume of a Cube: The volume $V$ of a cube is given by:

$V = s^3$

Now that we know $s = 4$ cm, we can find the volume:

$V = 4^3 = 64 \, \text{cubic centimeters}$

Thus, the volume of the cube is 64 cubic centimeters.

Would you like further details or have any questions?

Here are some related questions to explore:

1. How would the volume change if the surface area were doubled?
2. What is the relationship between the side length and surface area of a cube?
3. How do we calculate the diagonal of a cube's face given its side length?
4. How would you find the surface area if you were given the volume instead?
5. Can this method be applied to other polyhedra with different surface area formulas?

Tip: Remember, for any regular polyhedron like a cube, all sides are equal, simplifying many calculations involving surface area and volume.