What does "clean cut whimsy" mean?

Hello everyone. Non-native speaker here. Could you please explain me what does "clean cut whimsy" mean? I truly have no idea. I'm trying to understand this figure of speech word by word, but it doesn't work. Maybe someone could rewrite this phrase to make it more clearly?

The Cosby Show was wildly popular for a reason: it executed the family sitcom formula better than any other program. The stories were moralizing but plausible, the laughs were genuine, and the cast was solid from top to bottom. Though he’s become less universally beloved in his later years, Bill Cosby is undeniably one of the most talented comedians ever to grace the American stage, and he carried the show that bore his name with his finely honed brand of clean cut whimsy.