There's sweets at one end of the room, cubs with canes and string at the other. Guess what comes next.
Canes, string, sweets
Give the sixers and seconders an introduction/refresher to simple lashings while the other cubs play elsewhere. Then place the sixes at one end of the hut and the cubs at the other, and they have to figure out how to get the sweets without actually being able to go over and pick them up. Use tape or chalk to mark a boundary line on the floor which they can't cross. If they do cross, any sweets they've collected are returned to the far end. To add challenge, the sixers and seconders can't actually do anything themselves on the final structure. They can demonstrate and explain knots and lashings to the other cubs using spare bits of cane and string, and they can direct and supervise, but they can't take an active role because then they'd just do it themselves.