Sounds like you've got a short somewhere. You'll need to work methodically to track it down. It will help if you have a wiring diagram, so that you can identify everything that's linked to that fuse.
Are you able to easily disconnect the new radio, just to make sure it's not part of the problem?
If it was me I would start by removing all of the bulbs and see if the fuse still blows. That will tell you if it's in the loom or the taillights.
If it doesn't blow, add one bulb at a time (and removing each one as you go), to see if it's one particular bulb/socket that's causing the problem.
Good luck.
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