I'm working on a project which involves a mini talkbox.

I want to send a square wave using the tone library

I don't know what a talkbox is, but is a square wave OK?

Power is Voltage x Current.

Current is Voltage/Resistance or impedance (Ohm's Law).

From that you can derive Power = Voltage

^{2}/R.

A "regular DC" square wave is off half the time so that's half the power, so if you calculate 9V

^{2}/8 Ohms = 10W so that's 5W into the speaker. (With regular audio AC sine waves you get even less power from a given voltage.)