They will eat almost anything (broccoli, cheese, yogurt...) Their favourite foods are foods native to their dry habitat, like seeds, cereals, nuts, but make sure that it's natural seeds - no roasting or salt, and that the cereal isn't sugary.
For protein and variety, they will eat some small insects and egg-white. They like vegetables, but don't feed them too many, as they might suffer from a tummy upset and have sever diarrhea. You might want to give them a dog biscuit or pellets to chew on - it's healthy for them and is great for their teeth.
Try not to shock them too much. Give them a regular diet - like a commercial small animal mix - but supplement it with treats to give them some variety. Make sure as well that the food is still good to eat. Be sure that vegetables, bread, and other perishables aren't moldy or rotten.
Besically, hamsters eat almost anything. But there are some food which are bad for them and we, as their owners, must not give them that. Here are some examples to things which we are not supposed to provide it to them.
Do not feed them: Canned or frozen veggies, anything humans won't eat, raw beans, sprouting potato buds, onions, garlic, or toffee. Chocolate is a bad idea too, but there is a special variety of chocolate that's sold at pet stores that is safe for animals.
Hamsters The Essential Guide - The essential care and feeding of your pet hamster.
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