What is the side lengths in inches of a cube with a volume of 1 cubic inch?

A) It takes 228 more cubes of 1/3-unit length to fill the prism than the 1/2-unit length cubes.
B) It will take 768 1/4-unit length cubes to fill the prism.

A cube with 1/2-unit side length will have a volume of 1/2(1/2)(1/2) = 1/8.  Dividing the volume by this, 

12÷(1/8) = 12×(8/1) = 96 cubes

The volume of the 1/3-unit length cubes would be 1/3(1/3)(1/3) = 1/27.  Dividing the volume by this gives us
12÷(1/27) = 12×(27/1) = 324

This is a difference of 324-96 = 228.

The volume of the 1/4-unit length cubes would be 1/4(1/4)(1/4) = 1/64.  Dividing the volume of the prism by this gives us
12÷(1/64) = 12×(64/1) = 768