1. **State the problem:** We want to find what fraction of the volume of a 1-inch cube is occupied by one smaller cube with edge length 1/3 inch. 2. **Formula for volume of a cube:** The volume $V$ of a cube with edge length $s$ is given by $$V = s^3$$ 3. **Calculate the volume of the large cube:** The large cube has edge length 1 inch, so $$V_{large} = 1^3 = 1$$ cubic inch. 4. **Calculate the volume of the small cube:** The small cube has edge length $\frac{1}{3}$ inch, so $$V_{small} = \left(\frac{1}{3}\right)^3 = \frac{1}{27}$$ cubic inch. 5. **Find the fraction of the volume:** The fraction of the large cube's volume occupied by one small cube is $$\frac{V_{small}}{V_{large}} = \frac{\frac{1}{27}}{1} = \frac{1}{27}$$ 6. **Interpretation:** One 1/3-inch cube is $\frac{1}{27}$ of the volume of the 1-inch cube. 7. **Additional note:** Since the large cube is subdivided into smaller cubes of edge length 1/3 inch, the total number of such small cubes fitting inside is $$\left(\frac{1}{\frac{1}{3}}\right)^3 = 3^3 = 27$$ which matches the given information. **Final answer:** One 1/3-inch cube is $\frac{1}{27}$ of the volume of the 1-inch cube.