Well, thinking back to the passages that introduced the Mouth of Sauron, we see:
Quote:
Originally Posted by J.R.R. Tolkien
And he entered the service of the Dark Tower when it first rose again, and because of his cunning he grew ever higher in the Lord's favor; and he learned great sorcery, and knew much of the mind of Sauron....
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Makes it sound like the Mouth of Sauron learned "sorcery" during his time at Barad-dûr.
Now there's an interesting thought: what kind of education do they give you at Mordor?
Torture 101 with Professor Khamûl. Or
Metallurgy 243: The Forging of Morgul Blades, with a mandatory lab component.