Yes, they can do. Usually this would only happen if there was something wrong with the baby, and it would not be able to survive anyway. Try to stay away from your hamster soon after it has babies to avoid stressing her which can make her more likely to do this. You should always separate the father hamster from the mother and babies.
ummmmm...... well my friend gto 2 hamsters and found out 3 days after buying them one gave babies and the other hamster ate almost half of them so i guess they do except it was not the mother but they were both fighting over the babies to try and see who would keep and take care of them!(it was very sad!)