Quote by mfb
You can define g' such that the potential energy is mg'h, but this would be an odd definition as the density of the object would contribute to g'. I would change m to m' which is the difference of the mass of the object and the corresponding mass of water. If you just know the density, but not the total mass or volume of the object, all you can calculate is an energy density: ##\frac{E}{V}=\rho'gh = (\rho_{object}\rho_{water})gh## where ρ are density values.

Here is another way that I tried where I copied the formula from the web;
Net Gravitational Acceleration g' 0.315072129 m/s2
1p'/p 0.032128514 m/s2
Object Density p 996 kg/m3
Fluid Density p' 1,028 kg/m3
Buoyant Force Fb 1,013,473 N
The idea was that I could back in F=MA and multiply the Buoyant Force * g' * the mass and come up with the energy potential. Should I put in m'  the differential mass  instead of the mass?