Welcome here! This is a list of different types of litters and the pros/cons of each. This is from HRS:
Pros and cons of the various types of litter include:
clay litter is dusty–if your bunny is a digger, the dust can make her vulnerable to pneumonia
the deodorant crystals in some clay litters are toxic
clumping litters will clump inside the rabbit’s digestive and respiratory tracts (the latter if they manage to make enough dust to breathe) causing serious problems and often leading to death
pine and cedar shavings emit gases that cause liver damage when breathed by the bunny
corn cob litter isn’t absorbent and doesn’t control odor, and has the the risk of being eaten and casing a lethal blockage.
oat- and alfalfa-based litters (available from Purina, Manna-Pro, and King-Soopers groceries [not sure what the geographical range of this chain is]) have excellent odor controlling qualities, but if a rabbit eats too much, they expand and cause bloating; these, too, can be added, with the bunny’s waste, to compost
newspapers are absorbent, but don’t control odor
citrus-based litters work well, offer no dangers, and can be composted, but may be hard to get and expensive in some areas of the country/world
some people have reported success with peat moss which can also be composted
Many people have great success with litter made from paper pulp or recycled paper products. These litters are very good at absorbing and cutting down on odors. A litter called CAREfresh is available at most pet stores. A similar litter in a pelleted form is called Cellu-Dri 1-800-382-5001. These litters are harmless if ingested.
Compressed sawdust pellets are inexpensive, highly absorbent litters used in many foster homes. They are made from softwood or hardwood sawdust, but they are not toxic because the phenolic compounds are removed during their manufacture. Their wood composition helps control bacterial growth and odors. Wood stove fuel pellets and Feline Pine are two examples of this product.
Litters made from Aspen bark are safe and good at absorbing odors. One brand is called GentleTouch 1-800-545-9853.
The bolding above is mine. At the very least, cedar shavings should not be used with small animals ever. So I would suggest you remove those right away. Here is another article explaining why they are not safe: http://rabbit.org/litterboxes-and-liver-disease-2/
The cat litter may or may not be safe. It depends what it is. Clay litter, clumping litter, and the little gray “crystals” are not safe for rabbits. If the cat litter is a wood pellet (not shaving) or a paper-based litter, it is probably fine to use.
Many of us eventually start using wood stove pellets or horse stall bedding. It’s very absorbent, controls odor, and is seriously DIRT CHEAP. Maybe look into that?
EDIT: ALSO, you don’t want any type of litter/bedding in the BOTTOM of the cage, ONLY in the litterbox. Rabbits prefer laying on the plastic bottom. This will also encourage him to start doing his business in his litterbox.
If he’s having issues with using the litterbox or with odor, neutering will help with that. This can be done once his testicles descend, between 3-5 months.