Answer
See explanations.
Work Step by Step
Step 1. Identify the given conditions: smaller cube $V(x)=x^3$, larger cube $V(x+2)=(x+2)^3$
Step 2. Use the Binomial Theorem to expand the volume of the larger cube as: $V(x+2)=x^3+3\times2x^2+3\times2^2x+2^3=x^3+6x^2+12x+8$
Step 3. Calculate the difference: $V(x+2)-V(x)==x^3+6x^2+12x+8-x^3==6x^2+12x+8$ cubic inches.
