1. **State the problem:** We need to find the length of one edge of a cube given its volume is 64 cm³. 2. **Formula:** The volume $V$ of a cube with edge length $s$ is given by: $$V = s^3$$ 3. **Apply the formula:** Substitute $V = 64$ into the formula: $$64 = s^3$$ 4. **Solve for $s$:** To find $s$, take the cube root of both sides: $$s = \sqrt[3]{64}$$ 5. **Calculate the cube root:** Since $64 = 4^3$, we have: $$s = 4$$ 6. **Answer:** The length of one edge of the cube is 4 cm.