Answer: 15 cubic inches
Step-by-step explanation: If each cube measures 1/4 inch along each edge, then the volume of each cube is (1/4)^3 = 1/64 cubic inches.
If Jerome counted a total of 960 cubes, then the total volume of all the cubes is:
960 cubes x (1/64 cubic inches per cube) = 15 cubic inches
Therefore, the volume of the box that Jerome filled is 15 cubic inches.