By laminating sheets of cardboard together into a large block and cutting this up with a table, or circular saw, you can create cardboard lumber of any dimensions you want: 2x4s, 2x8s, 4x4s. If you alternate the grain of the corrugations you can create plywood. If you glue your lumber together end-to-end you can create strong honeycomb-like boards.
You will only need three things to create cardboard lumber:
1) A Saw
2) Lots of cardboard
3) Glue... lots of glue
Step 1: Types of Saws
Circular Saw: If you're really good at cutting straight lines and have no other option then I guess you could give it a try.
Hand Saw: Possible, but too labor intensive for me.
Band Saw: If your band saw is as powerful as a circular saw than go for it, this could open interesting options.
Chain Saw: Messy...
No Saw: Unfortunately for people without access to saws, this instructable is not for you. I know it looks cool and all, but it's just not gonna work out.