Outpost 8 was an outpost constructed on an asteroid by Starfleet in 2160.

In 2266, the Federation lost contact with the base. It was determined, by the USS Enterprise, that the station was destroyed by an unknown vessel that was later discovered to be a Romulan Bird-of-Prey. (TOS: "Balance of Terror")

Between 2266 and 2366, this base was rebuilt. In 2366, this outpost received a warning from Starfleet Command about an alleged Romulan base on Nelvana III. (TNG: "The Defector")

This outpost was only mentioned in dialogue.
According to Star Trek: Star Charts (p. 66) and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), Outpost 8 was located in the Beta Quadrant.
In the Star Trek: Star Charts (p. 66), the location of 23 Earth outposts were depicted on a map of the Beta Quadrant. Outposts 1 to 8 were mentioned in dialogue or were seen on the Z-6 Sector map in "Balance of Terror" and Outpost 23 was mentioned in dialogue in "Future Imperfect".
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