1. The problem asks to find the length of a cube given its volume is 3375 cm³. 2. The formula for the volume of a cube is $$V = s^3$$ where $s$ is the length of a side. 3. To find $s$, we take the cube root of the volume: $$s = \sqrt[3]{V}$$. 4. Substitute the given volume: $$s = \sqrt[3]{3375}$$. 5. Calculate the cube root: $$3375 = 15^3$$, so $$s = 15$$ cm. 6. Therefore, the length of the cube is 15 cm.