The torturer is Brad's kidnapper who wears a gold mask. In Heavy Metal Musical, he reveals himself to be Padraig Skelly and a lich.
Brad the Bard was a performer at the Bannered Mare rivaling fellow bard Mikael. Brad was kidnapped by an unknown man with a mask on and was held in an icy cavern. (Starting in the episode Pastel HELL) The torturer would put Brad in a cage and shoot arrows and cast destruction spells on the bard in order to make him sing songs for the segment Songs of Skyrim.
Cock Nibbler does not realize Brad was being tortured until Heavy Metal Musical (S6E30). Cock goes to the Bannered Mare to find Brad missing. He finds a note on the counter labeled, FOR COCK'S EYES ONLY. It's a note left by Brad's kidnapper and directs Cock to go to the Mysterious Cave near Solitude.
Upon arrival, Cock, Brad, and the lich battle with their voices and sing to their tunes. Brad sings a ballad; the lich sings metal; and Cock sings amateur. But as soon as the vocal battle ends, the physical battle starts. Cock Nibbler, without divine protection from the Game Society Pimps gods becomes overpowered by the lich.
The lich dies after Brad the Bard heroically smashes the crystal containing its soul.