Final answer:
Advanced algebra can indeed provide a way to construct a cube with double the volume of another using only a straightedge and compass, thanks to understanding the relationship between side lengths and volume.
Explanation:
Constructing a cube with double the volume of another cube using only a straightedge and compass was proven possible by advanced algebra. When dealing with cube volumes, the relationship between side lengths and volume is crucial. For instance, to create a cube with double the volume of another, you need to consider the cube root relationship which affects the change in volume.
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