Here's you pin map:
You have Ports A, B, C, D with pins as SAM3X pin names PA##, PB##, etc.
If you can get 16 pins in a row on the same port then you should be able to write 16 bits to that port in one go. Once the bits are written however you do it, the pins should reflect what you wrote. It's a lot quicker than setting 16 pins 1 at a time.