1. **State the problem:** We need to find the surface area of a cube-shaped box with side length 8 cm. 2. **Formula:** The surface area $S$ of a cube with side length $a$ is given by: $$S = 6a^2$$ This is because a cube has 6 faces, each a square with area $a^2$. 3. **Calculate:** Substitute $a = 8$ cm into the formula: $$S = 6 \times 8^2 = 6 \times 64 = 384$$ 4. **Answer:** The surface area of the box is $384$ cm². Therefore, the correct choice is B. 384 cm².