The only time* Brian Epstein was mentioned in the old 60's Beatles cartoon TV show was in Episode 3A, "PLEASE MISTER POSTMAN" (locale - Africa)
Summary: The Beatles are all out of money and starving, thanks to Ringo buying rings that are immediately handshaken off him.
Ringo attempts to "wire" Brian Epstein by drumming on a log! However, he forgets to reverse the charges.
Dialogue from George: "If the operator wants ten pounds, I'll give her ten pounds!" (Grabs stick from Ringo and "pounds" the log) "One, two, three - "
The postman finally arrives, during their concert, but instead of money they receive an overdue notice from the Liverpool Light Company.
-(posted in newsgroups rec.arts.animation and rec.music.beatles by Howard Fein on 7/9/2004)
*Eppylover correction: A Beatle fan's webpage claimed there was indeed another mention of Brian in one other episode in this series, Thank You Girl. However, when I found it on YouTube, "Brian" turned out to be an unnamed, unseen man sitting in a pink chair All you can see is a hand holding a cigar. The voice was distinctly American. Please see THIS POST for details.