Although the details were quickly pulled, it seems as if the existence of LittleBigPlanet 3 may have been inadvertently confirmed.
The unannounced sequel appeared on the CV of JK Studios animator; although the link has since been wiped, a cached version was available at time of writing.
The animation studio apparently did some work for Sumo Digital on the project. The independent Sheffield developer produced Moshi Monsters, and does jobbing work for Sony among other clients; we were told Sumo was working on LittleBigPlanet 3 in February this year.
The CV does not give a release date or platforms, but we had learned that the project had been on the go for over a year, so it’s at least 18 months old by now. We might see something during Sony’s E3 press conference.