USS Enterprise computer core, late 2260s
The computer core (or memory core) was the location of a starship's or space station's central computer.
The computer core housed primary processing equipment including the computer core processors. 23rd century Starfleet ships had duotronic systems, while 24th century ships had isolinear cores. The computer cores communicated with each other and ship's systems via an optical data network (ODN).
Galaxy-class computer access room and core, c. 2360s
The Galaxy-class of Federation starships carried three computer cores, while ships of the Excelsior-, Intrepid-, and Sovereign-classes contained two. These multiple cores provided redundancy in case one of the cores was damaged or destroyed.
The computer core could be accessed by the computer access room. (TNG: "Evolution")
In 1996, Henry Starling managed to download almost twenty percent of the USS Voyager's computer core to his personal computer by using the ship's transporter beam as a downlink. (VOY: "Future's End", "Future's End, Part II")
According to Commander Charles Tucker III, the computer core of Enterprise NX-01 was three decks high and was, as of 2152, the most powerful computer ever created. (ENT: "Dead Stop")
Location of the computer cores aboard the Enterprise-B
In 2293, the location of the computer cores aboard the Excelsior-class USS Enterprise-B were labeled in a MSD. These cores were located in the primary hull, on decks 7 to 9. (Star Trek Generations)
After beaming aboard the IKS Drovana to obtain the detonation codes for a Klingon minefield in 2372, Worf and Kurn told an officer they were running a diagnostic on the starship's computer core. (DS9: "Sons of Mogh")
In 2373, Worf told Nog to load the files of a phaser relay operating system into the USS Defiant's computer core. (DS9: "Soldiers of the Empire")
In order to take Deep Space 9's computer systems offline and prevent the Dominion from destroying a minefield covering the Bajoran wormhole, Kira Nerys and Rom considered planting a bomb in the station's computer core. They later attempted to sabotage it by more standard means. (DS9: "Sacrifice of Angels")