What if there is an error message that adoptopenjdk8 exists in multiple taps?
Here is a quick solution which assumes that Homebrew is up-to-date and there is no need to use any other packages from the adoptopenjdk/openjdk tap:

Check the state of adoptopenjdk/openjdk tap and adoptopenjdk8 package:


brew tap - lists which taps are currently enabled
brew search adoptopenjdk8 - shows which adoptopenjdk8 casks are available from the enabled taps and which adoptopenjdk8 casks are currently installed


Now assuming that the adoptopenjdk/openjdk tap is listed as enabled, remove the adoptopenjdk/openjdk tap as follows:

brew untap adoptopenjdk/openjdk


Then check what adoptopenjdk8 casks are currently installed. This should show exactly one adoptopenjdk8 cask installed.

At this point, brew cleanup should work correctly.

My explanation: it appears to me that they added adoptopenjdk8 to the built-in Homebrew caskroom.

Note that it should be OK to do brew tap adoptopenjdk/openjdk afterwards, if needed. (This has not caused any issues for me so far.)