Write an expression for the volume of the box shown in

Exercise 37 if the dimensions of each side were doubled.

We don't see your diagram, but it doesn't matter.

Suppose the dimensions were l by w by h
volume is lwh

after doubling:
new dimensions are 2l by 2w by 2h
new volume =(2l)(2w)(2h) = 8lwh

So doubling the dimensions of the box will increase the volume 8 times.