The font used for Facebook's logo is very similar to Klavika Bold, which is a square sans serif font designed by Eric Olson and published by Process Type Foundry. Here's the download link.

Eric Olson is a typeface designer and founder of the Process Type Foundry, an independent type design studio based in Minnesota. Inspired by the underground punk rock scene of the '90s and the DIY spirit of magazines like Emigre, he began designing typefaces for his own use and later launched the foundry in 2002. The studio has since become known for dependable and hard-working typefaces like Klavika, Colfax and Maple. In addition to retail offerings, Eric has designed custom fonts for the New York Times magazine and Thomson Reuters, among others.