Black Bolt, the Inhuman king, does sleep. While his powers are immense, he still requires rest like any other living being.
It's important to note that Black Bolt's sleep patterns may be different from humans. His physiology is unique, and his powers could potentially influence his sleep needs. However, he has been shown to sleep in various Marvel Comics stories and adaptations.
For example, in the Inhumans TV series, Black Bolt is seen sleeping in his chambers. He also appears to sleep in the Black Bolt comic series.
While the specifics of Black Bolt's sleep patterns remain largely unexplored, it's clear that he requires rest to maintain his physical and mental well-being.