A cube has maximum volume for a given perimeter.
So, it has minimum perimeter for a given volume.
This article may be helpful. A web search can provide many others.
https://math.stackexchange.com/questions/1224787/proving-cube-volume-larger-than-box-volume-with-a-constant-surface-area
Find the dimensions of the rectangular box of volume vθ for which the sum of the edge length is least.
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