Google has made a change to their YouTube platform so that users can now cast live videos to their Chromecast devices. This new feature only works when users are accessing YouTube using their desktop web browser where they will find the cast button now available on live streams. This capability is not yet enabled when using the YouTube app on a smartphone or tablet, but it seems like it should not take long for an update to roll out to enable this on mobile devices.
Google also recently changed the YouTube site to allow the casting of private YouTube videos. It appears that the only type of video that cannot be cast from YouTube are those where the publisher has not enabled viewing on mobile devices.
source: Android Police