I have a 7500 sq ft home, it requires a 200 amp main, I have three floors and was wondering how many sub panels could I run off a 200 amp main?

I fixed the title, you had watts when you meant amps.

You may have as many loadcenters (AKA subpanels) fed by the Main Panel as desired.

For a 3 story structure, one per floor would suffice, and assuming the Main Panel is in the basement, that would give you a panel per level for those branch circuits on each floor.

Has a service rating load calculation been done, to determine if a 200 Amp service is adequate for this home?

My gut tells me it is not. But calculations would tell.

Just for lighting alone at 3 watts per square foot is 93 amps, less any applicable derating factors. Add appliances, heat, air conditioning, unless everything is gas, 200 amps is not enough.

I agree with TK. I find it hard to believe that the load calc is under 200A.

Is this home under construction?