1. **State the problem:** We need to find how many cubic boxes of dimension 50cm × 50cm × 50cm can fit into a storage room of dimensions 4m × 2m × 4m. 2. **Convert units:** Since the box dimensions are in centimeters and the room dimensions are in meters, convert the room dimensions to centimeters. $$4m = 400cm, \quad 2m = 200cm, \quad 4m = 400cm$$ 3. **Calculate the volume of the room:** $$\text{Volume}_{room} = 400cm \times 200cm \times 400cm = 32,000,000 \text{ cm}^3$$ 4. **Calculate the volume of one box:** $$\text{Volume}_{box} = 50cm \times 50cm \times 50cm = 125,000 \text{ cm}^3$$ 5. **Calculate how many boxes fit by volume:** $$\frac{\text{Volume}_{room}}{\text{Volume}_{box}} = \frac{32,000,000}{125,000} = 256$$ 6. **Check fitting by dimensions:** Number of boxes along length: $$\frac{400cm}{50cm} = 8$$ Number of boxes along width: $$\frac{200cm}{50cm} = 4$$ Number of boxes along height: $$\frac{400cm}{50cm} = 8$$ 7. **Calculate total boxes by fitting:** $$8 \times 4 \times 8 = 256$$ **Final answer:** $$\boxed{256}$$ boxes can fit into the storage room.