Take taming slowly and with patience. He is giving you a message that he feels stressed by your hand in his cage. They need to learn to trust. It would be better to do taming out of the cage, gradually. You could get him out in a tube - put a treat in one end and put the tube in front of his house (treat at far end). When he walks in put your hands over both ends of the tube (wear gloves so you don't get nervous and drop him if you feel him push at your hands but it would be hard to bite at that angle!) and lift the tube out carefully, then put it down into a secure box nearby and let him out. You can then transport him to the dry bathtub for some taming sessions. If you have a hamster ball, an easier way is to put one end of the tube in the hamster ball and let him walk into it then pop the lid on and carry him to the bathtub that way.
It's important to be very gentle when handling them so they learn to trust that you won't hurt. Stress and cage rage can also cause them to be aggressive, so is your cage big enough? If you have a photo we can advise because sometimes, even when it is big enough, the level of enrichment or layout isn't right for them so they don't feel safe.
Just adding a video of when we tamed our last Syrian - it doesn't show much but has some tips. He was ferral when we got him and would run at your hand but once he trusted us and was tame he was soft as anything and would go to sleep on my knee.
Haha - the tips aren't showing up on the video. Basically let them run around in the bathtub with a few toys and they tend to slither up and down the side of the bath trying to get out. Occasionally stroke her on the back lightly with one finger - just one stroke (you can wear gloves). If she jerks round to bite or actually bites, then stop. A few minutes later try again. Maybe do this two or three times first session. Continue with this each session (maybe every 2 or 3 days or 3 times a week) and eventually she will stop jerking round to bite your finger and will ignore it. This is a big step. Next move onto cupping a hand under her while she's walking round in the bathtub. Don#t try to hold her, just let her walk off again. After a few times of this, then next session cup your hand under her and lift it slightly - just 1cm or so. But still let her walk off. Then move onto lifting it slightly higher - 2 to 3 inches then lower her down again. By then you should be able to pick her up and hold her for short periods and let her run from hand to hand with your hands tunneled. Don't do it for too long or they get frustrated. Our hamster was tame as anything once we could pick him up. But even then he didn't like being handled for too long.
Generally they also don't like a hand in their cage as it's their territory.