The volume of the rectangular prism is $8 \times 2 \times 32 = 512$ cubic inches.
To find the side length of the cube, we take the cube root of the volume: $\sqrt[3]{512} = 8$ inches.
The surface area of a cube is given by $6s^2$, where $s$ is the side length.
So the surface area of the cube is $6 \times 8^2 = \boxed{384}$ square inches.
The answer is: 384
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
A rectangular prism has dimensions 8 inches by 2 inches by 32 inches. If a cube has the same volume as the prism, what is the surface area of the cube, in square inches?

### Answer:
