Final answer:
The difference in volume of the small and large cubes is 64x^6 - 216y^3.
Step-by-step explanation:
To find the volume of a cube, you need to raise the length of one side to the power of 3. In this case, the small cube has a side length of 6y, so its volume is (6y)^3 = 216y^3. The larger cube has a side length of 4x^2, so its volume is (4x^2)^3 = 64x^6. The difference in volume is obtained by subtracting the volume of the small cube from the volume of the large cube: 64x^6 - 216y^3.