1. The problem is to find the volume of a rectangular prism (in this case, a cube) with edge lengths of 5.1 inches each. 2. The formula for the volume $V$ of a rectangular prism is: $$V = l \times w \times h$$ where $l$ is length, $w$ is width, and $h$ is height. 3. Since this is a cube, all edges are equal, so: $$l = w = h = 5.1$$ 4. Substitute the values into the formula: $$V = 5.1 \times 5.1 \times 5.1$$ 5. Calculate step-by-step: $$5.1 \times 5.1 = 26.01$$ 6. Then multiply by 5.1 again: $$26.01 \times 5.1 = 132.651$$ 7. Therefore, the volume of the cube is: $$\boxed{132.651 \text{ in}^3}$$ This means the cube occupies 132.651 cubic inches of space.