Yes, each box will need an invoice attached to its exterior. However, you can create one invoice for all the contents of the boxes and attach a copy of the invoice to each box. You can then just number each box eg. (1 of 5), (2 of 5), (3 of 5) etc.
We also recommend that you provide our staff with a copy for quick review. Be sure that the total retail value of the boxes does not exceed $800 USD if they are all going to the same address.