Anyone know why brake lights don't work but rear cab light lights up on a 2007 Chevy Silverado 2500HD pickup?

you might have a fuse blown or the wire to your rear lights is broken somewhere. i would start by checking the bulbs and if they are ok move on to tracing the wires back to there source and make sure the lines are ok

Deathjam is correct. I would also look at the trailer brake wiring, brake light switch (its up under the dash where the pedal mounts to the firewall) any connectors near the brake lights.