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You should clean the cage when your ham is awake ideally, it's best to put the hamster in a carrier with plenty of substrate inside while you do the cleaning, don't try to clean the cage while the ham is in there as that can be very stressful for them.
You probably won't need to clean the whole cage monthly, you do need to spot clean pee on a regular & fairly frequent basis but only clean the rest of the cage if it really needs doing & always put back some of the old substrate when you clean so your hams cage still has it's scent, don't clean the nest unless you really have to & always put back some of the old nest material, same goes for the food hoard your ham will make, if it has any fresh food like veg in it you may need to clean it out but then just put some more hamster food back in the same place.