Laputa is a flying island or rock, that can be directed by its inhabitants in any direction. Its tyrannic ruler uses it to control the mainland by threatening to cover rebel regions with the island's shadow. The people of Laputa are fond of mathematics and technology, but fail to make practical use of their knowledge. They created such marvels as a mirror that would let you converse with any historical figure, but couldn't construct well-designed clothing. This is probably a satire on the Royal Society.
The "Laputa Missile Complex" is the target of the B-52 bomber "Leper Colony" in the 1964 satire Dr. Strangelove, a reference to the highly theroetical discussions of nuclear war and deterrence that led the world to catastrophe in that film.
The 1986 anime film Laputa: The Castle in the Sky by Hayao Miyazaki features a floating city named Laputa after that of Gulliver's Travels.
"La puta" means "the whore" in Spanish. Swift probably knew this, and Miyazaki probably not. The Walt Disney company did, and as the American distributor of Miyazaki's film (though still unreleased in the USA), contracted the name to "Castle in the Sky." Some Spanish editions of "Gulliver's Travels" use "Lupata" as an euphemism.