In the SI system, watt is the unit for power. Hour is a unit of time, equal to 3600 seconds. Power is the energy expended per unit time, or power = energy/time. Energy = power*time. Watt-hour is therefore a unit of energy. Watt hour squared is energy multiplied by time. One Watt-hour is equal to 1*60*60 = 3600 Amperes. One ampere represents the passage of one coulomb of charge per second.
One watt-hour squared = 3600 amp*hour = 3600^2 amp*second = 3600^2 (C/s)*s = 3600^2 coulomb.
The watt-hour squared can be taken as a unit of electric charge.