Don't forget to factor in the humidity of the air. The more humid the air is the less dense it is. After all where are you going to find a cubic mile of dry air to fill the box?
@DB showed how simple it really was to do. His answer was 5,218,836.48 tons.
This is nine significant figures, using STP (standard temperature and pressure, viz. zero degrees celsius and 760 Torr, or 14.7 PSI at sea level). The whole point was to demonstrate how ENORMOUS is the weight of air. Many people guess "nothing. Air is weightless," they say.
If that were the case, aircraft could not fly. Nobody ever guesses a weight as huge as five million tons.
The humidity of air is highly dependent on the temperature. At twenty-five degrees Celsius, the difference in density between dry air and saturated air is on the order of 1 or 2 percent. It's lost in the long line of numbers of tons.
https://www.engineeringtoolbox.com/density-air-d_680.htmlThere is no need to "find" dry air. It's all a mind exercise. No such box will ever exist, much less a scale with which to weigh it.