The mass of the cloud when the cloud starts to form is different from the mass of the cloud when the cloud is fully formed.
It is because at the start, the size of the cloud is extremely small in size, so the mass would be smaller as well.
As the size of the cloud becomes larger, the mass of cloud would also increase as well.
This means that instead of the cloud itself being moved, it is closer to the cloud growing in size, thus giving the appearance of said cloud expanding.
Using CAPE values in the original calc, and using 0.5 grams/m^3 for density, we get:
Volume = Pi x height x radius; using cylinder
Density = 0.00005 kg / meters^3
Mass = Density x Volume
Mass = 0.0005 x 3.1416 x (12,000) x (3,600)^2 = 244,290,816 kg
But then condensation happens in cloud formation, as clouds are generally liquid particles suspended in the atmosphere.
"Condensation is the process by which water vapor in the air is changed into liquid water."
Latent heat of condensatio = 2,500.8 J/gram, or 2,500,800 J/kg
Energy required for condensation = (244,290,816 kg) x (2,500,800 J/kg)