Gelly,
Does this happen when you are home only? Does it happen at a certain time of day?
It could be a ploy for attention. Though you do not have rugs he can get around on the floor. You just need to watch him, they can learn to be on slick floors but they need to be watched closely. You can also try spreading some fleece on the floor and give him a bit more room, while watching him of course.
I bet he wants attention when he is doing it. My few that chew are usually telling me they want attention or sometimes they want more hay/food.
Be careful "rewarding bad behavior". If you don't want him chewing the bars or pushing/pulling the cage don't give him attention. When he stops, you can go over and talk to him, ask, "Do you want attention?" Reach down and pet him, open the cage and sit near him, etc. Just don't do it when he is chewing the cage/moving it because he will eventually associate attention with that bad behavior.
You can try telling him "NO" or if you have a way to "reprimand" him when he is doing the bad behavior - put him in the bathtub, or something like that; so he associates something he doesn't like with that behavior. Rabbits, especially young ones, tend to be like toddlers...good luck, hopefully there is something that works that you read.