I may be missing something, but I don’t see what the cube root has to do with this calculation.
I think a cube root is part of SpongeBob’s family tree, or somethin’.
This whole thing is about the author stating cubic meters when it would seem obvious that he meant a much larger number; since metric measurements are denoted with common prefixes we feel compelled to think he meant kilometers.
To appreciate a volume one needs to be able to make a picture ; if we have a 100 cu ft regrigerator in the shape of a cube we intuitively recognize that it is constructed with 10 foot sides, tops and bottoms or that we could stuff 100 one cu ft boxes in it.