Length Ratio of a Cube/Cuboid

No such ratio exists. A cube of twice the side length has eight times the volume. However, you can say that the side length of a cube is the cube root of its volume.

If by "cuboid" you mean "rectangular prism", then the situation is even worse than for a cube, since there are infinitely many configurations with different measurements that all give the same volume.
You could use length and volume scale factor

Construct the most simple cuboid from your ratio, say 3x2x6 which will have a volume of 36 units^(3)

Then you know some scaled version of your constructed cuboid has volume 50 units^(3)

That means we scale the volume by 50/36=25/18 so each side length must be scaled by (25/18)^(1/3)

Work out each side length, and work out the product to check you get 50 back at the end

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