Give the Cubs different materials to build a small bridge.  You can give them specific challenges (e.g. must hold the weight of a can or some coins, must span a certain distance, must be a certain height).  You can mix up the materials and give each group a different set of materials or they can select for themselves what they want to use.  Alternatively, provide them all with the exact same items and make it a competition of sorts.

The Da Vinci bridge design is an option using sticks, staves or popsicle sticks to show a self-supporting bridge with nothing holding the sticks together.  

HOW TO MAKE A DA VINCI BRIDGE // Full-size Leonardo Da Vinci bridge - YouTube