Not sure about youtube, but for the right age kid, maybe late-elementary to early high school, there's a weekly "Joyful math jamboree" online. The web page for

Not sure about youtube, but for the right age kid, maybe late-elementary to early high school, there's a weekly "Joyful math jamboree" online. The web page for it is not updated very often, but the registration form still works. There's also the Julia Robinson Math Festival that's supposed to be good but I don't have first-hand experience. Ideally, a Math Circle would could be good for some kids if your area supports one.