To determine the surface area of the cube, follow these steps:

Step 1: Calculate the side length of the cube

The volume of a cube is given by:

$V = a^3$

where $a$ is the side length of the cube. Given $V = 64 \, \text{cm}^3$, solve for $a$:

$a = \sqrt[3]{64} = 4 \, \text{cm}$

Step 2: Calculate the surface area

The surface area of a cube is calculated as:

$\text{Surface Area} = 6a^2$

Substituting $a = 4 \, \text{cm}$:

$\text{Surface Area} = 6 \times (4)^2 = 6 \times 16 = 96 \, \text{cm}^2$

Final Answer:

The surface area of the cube is:

$\boxed{96 \, \text{cm}^2}$

Would you like further clarification or additional details?

---

5 Related Questions:

1. What is the formula for the volume of a rectangular prism, and how does it differ from a cube?
2. If the cube’s surface area was given instead, how would you calculate its volume?
3. How does the volume change if the side length of a cube doubles?
4. What are the units for volume and surface area, and why do they differ?
5. How can the concept of a cube's surface area be applied in real-life situations, such as packaging?

---

Tip:

When solving problems involving cubes, always ensure that you’re using consistent units for all dimensions and clearly differentiate between volume ($\text{cm}^3$) and surface area ($\text{cm}^2$).