What size wire must be run for 6 - 30amp sub pannels 350' away from 100 amp main?

Will the six additional panelboard be in the same building or are they going to be in outside buildings?

You do understand that you are going to be pulling a maximum of 180 amps away from a 100 amp main panelboard.

Without additional information from you, I would speculate that you need 4 ea. of #8 copper conductors. This is ONLY if the conductors are inside the same building.

I do not know why if the wiring is inside or outside would make a difference regarding voltage drop.

To do voltage drop calculations, need to know the supply voltage and the actual load in amps or wattage.

Assuming 240 volts at 30 amp load, #4 copper is needed.

If 120 volts at 30 amps, then #1 copper wire is needed.

Can you explain further why 6-30 amp feeders are needed to go 350 feet?

Knowing whether the wiring is inside or not will further define the method for grounding at the secondary panelboards.

T.K. What wire size calc are you using? I set mine to 240/30 using copper. The distance was 350' and it comes up with #8 conductors (voltage drop of 6.8%)