In my former position, I did alot of shipping of course materials both domestically and internationally. One of the companys where I use to phone in orders for boxes of all shapes & sizes was: http://www.uline.com/
Hope it helps!
It is my understanding that you can use the "free" boxes for any air service, which includes 3 day select. You use the terminology of 3 day ground, which does not exsist, however you certainly will have ground packages that will arrive within 3 business days based on the zone you are shipping to. For example, if you are shipping to the east coast from CA it will take 5 business days using ground, if you want the shipment to arrive in three business days you would use 3 Day Select & be able to utilize the free boxes. I hope this makes sense.
If you are ordering boxes, I agree with Nicole`s prior response of using Uline.
Honey child is right. UPS is just one supplier of parcel post service. You might also try DHL of Fed Ex ground service. Also, if you are shipping within a geographic, you might find a local carrier with special rates for that area. I used to ship orders with a local freight service for example, from Las Vegas to Utah at a third of what UPS charged. Before you commit to one service, research all you options.