"Volumetric" scaling

Hi! Could someone tell me an equation for scaling an object basing one one value(mass) accordingly naturally. It is like object which weighs 1 kg should be scaled 1x1x1. I use obj.scaling = [x, y, z]. If I have 3kg heavy object, 3x3x3 scale will be too large. What equation to use to get correct proportions?

I have 2 ideas for this

  1. In object mode, scale the object times three to get the desired mass. Switch to edit mode and scale the object to .3 (or whatever your desired size is) that way the object is still 3-3-3 but the mesh is 1-1-1
  2. If you are using rigid body physics, there is a option called mass factor (or something similar) which I think can multiply mass.
    hope one of these ideas helps!

It was meant a bit different, but I guess scorpion81 told the answer. A cubic root from mass can be facter for each scale so:

scaling = mass**(1/3)
obj.scaling = [scaling, scaling, scaling]

This way proportions looks fine:
1 kg = 1 x 1 x 1
3 kg = ~1.44 x ~1.44 x ~1.44
0.5 kg = ~0.8 x ~0.8 x ~0.8

All theese scales are proportionally fine and does look quite real:)