V(p) = x-n, where V(p) is the volume after the boxes have been together, x is the volume of the larger box, and n is the volume of the smaller box.
x = 15 cm x 25 cm x 20 cm = 7500 cubic centimeters (cm^3)
n = 10 cm x 10 cm x 10 cm = 1000 cm^3
V(p) = 7500 - 1000 = 6500 cm^3
So your answer is 6500 cubic centimeters.