Joshua and Wendy are cleaning the storage shed to earn some spending money for the family vacation. They set aside five boxes to take to their bedrooms. Each box is a cube. The four smaller boxes are of equal size and, when stacked, match the height of the larger box.

Given that the volume of one smaller box is $216$ cubic inches, find the sum of the volumes of all five boxes (in cubic inches).

Let's think step by step and output the final answer within \boxed{}.
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