I don't know if it's worth the trouble or not, but you can sign up for a fed ex and I think ups account, it's free to sign up, they give you free shipping materials, and you get a big discount on shipping.
I'd look at the post office for one of those boxes that has a flat rate and doesn't matter the shipping weight. It would probably save you money that way.
Unfortunately no discount with an account unless you ship a LOT, like everyday. I know, because I used to ship an average of 30 packages a month, and still no discount. You do get free supplies, you can request them online, but they take a few days to get.
Neither shipper has a box that will fit a 3' x 3', though.
The USPS flat rate boxes are too small for your 3' x 3'.