There are several artists using this name:

1) B3 is an American boyband from New York who reached in Germany the largest popularity. The band split in December 2004.
Recording history:
* First (18. Solders 2002)
* N. Y. B3 (24. March 2003)
* N. Y. B3 Special Edition (17. November 2003)
* Living for the Weekend (27. September 2004)

2) B3 is a Serbian band which was popular in the '90s.

3) B3 (http://www.b3.sk/) is a Slovak pop band with various members —
Peter Graus, Tomáš Zubák, Ivan Hirländer and Marián Kachút (on some albums with a female singer — Tina)
Discography:
* B3
* Drobnosti majstrov
* Audiohead
* Be free for friends