Gilbert's last name has changed several times throughout the series. He it is Gates, later it's Bates, and still later, once in awhile, it's Harrison.
When the character Gilbert is introduced, his father, (at the end of the episode), explains his son is an only child. In the episode Beaver Joins a Record Club (1962), he mentions his brother and in the episode The Party Spoiler (1962) (among others), he talks about his sister.
Earlier in the episode, Gilbert mentions a brother (which is not true).
Earlier in the episode, Gilbert mentions a brother (which is not true).