How many cubic feet of air does my 16" tire hold?

The cubic feet of air remains the same with the tire, inflated or not, only the pressure changes.
Now, if you want to know how many cubic feet of air must run through an air compressor to inflate the tire to 70 psi, that is an entirely different question.
To add 70 psi is equal to 4.76 atmospheres so what ever the actual cubic feet of your empty tire is, (Guessing it to be somewhere around 2.2 cu. ft.) than it would take 2.2 x 4.76 or about 10.5 cu. ft of air compressed in to your tire to equal 70 psi.