Borg cube

In a parallel universe, the Borg cube was a type of huge cube-shaped starship and primary ship class of the fleet of the Borg Collective.

Battle of Wolf 359
A single Borg cube waged an invasion of the United Federation of Planets, its crew kidnapping and assimilating Captain Jean-Luc Picard of the Starfleet vessel USS Enterprise (NCC-1701-D). Formerly Picard, "Locutus of Borg" led this ship against the Federation at Wolf 359. Using Picard's knowledge of Starfleet tactics and weaknesses against them, the Borg inflicted staggering loses against the fleet in the Battle of Wolf 359, resulting in the loss of thousands of lives. During the battle, the Doctor's TARDIS made a brief trip to Locutus' cube. The Eleventh Doctor, accompanied by his companions, Amy Pond and Rory Williams, had travelled back from 2368 to acquire executive routines which would allow the Borg Collective to restore themselves and aid the Federation against their mutual enemy, the Cybermen.

After defeating the Starfleet task force, the Borg headed directly to Earth. Before its arrival, however, Data and Worf were able to retrieve Picard from the Borg cube and return him to the Enterprise as part of Commander William Riker's plan to turn the tables against the Borg. With the help of Captain Picard, Data was able to incapacitate the Borg cube and induce its self-destruction. (COMIC: Assimilation²)

Borg-Cyberman Alliance
In 2368, dozens of Borg cubes were part of the fleet of the Borg-Cyberman Alliance along with a Borg sphere and Cyber-ships of the Cyber-Armada. They were present at Delta IV in the Delta system, where the alliance overran the member planet of the Federation. The fleet was found by the Enterprise, which was immediately attacked and forced to retreat into the Paertes Nebula. The fleet then proceeded to Cogen V where, in the midst of assimilating the planet, the Cyber-Armada broke off from and overwhelmed the Borg forces. Soon after, the wreckage of many Borg vessels was found by the Enterprise, with Lieutenant Data determining that the majority of the Borg ships previously seen at Delta IV had been destroyed by the Cybermen. (COMIC: Assimilation²)

Behind the scenes
The Borg cube was the first and most common type of Borg ship to be seen in Star Trek, so much so that when the Borg appear, their cubes are rarely absent.