Litterbox training is definitely possible for most hedgehogs – however, it is important to understand that hedghogs have a limited capacity for litterbox training compared to, say cats. A hedgehog will very likely learn to reliably use a litterbox which is placed inside their own cage. The advantages to this set up is that it will greatly reduce the time and effort you as an owner will need to put into cage cleaning. However, many hedgehogs may not reliably use a litterbox exclusively when outside of their cage. For this reason you may want to keep your hedgehog to a restricted area with a litterbox to reduce confusion, gradually increasing available space overtime.
How to start litterbox training
First you will need to select a litterbox that your hedgehog can easily climb into. Look for a box that is about a foot square and only a few inches high. Fill the box with cat litter. Place the litterbox in your hedgehog's cage and then look for waste pellets in the bedding. Place any you can find in the litterbox to help your hedgehog realize that this is a place for using the bathroom. Alternately, if your hedgehog has a favorite bathroom corner in his or her cage, then simply place the litterbox in this spot and add the waste pellets.
If after placing the litterbox in your hedgehog's cage, your hedgehog still uses the bathroom in another location (which he or she will), simply have your hedgehog watch as you place the waste pellets in the box. Be sure not to scold if your hedgehog does not use the litterbox. Rather rely on positive reinforcement as much as possible.
Some hedgehogs will take to litterbox training right away whereas others will take longer, or not learn altogether.
Lastly, always remember to clean waste out of the litterbox on a regular basis and once a week take the time to replace all the litter and wash out the box.