Error: Cowardly refusing to 'sudo brew update'
You can use brew with sudo, but only if the brew executable is owned by root.
However, this is both not recommended and completely unsupported so do so at
your own risk.
MBA:bin root# ls -la /usr/local/bin/brew*
-rwxr-xr-x 1 taien admin 4913 Feb 11 20:46 brew
lrwxr-xr-x 1 taien admin 40 Oct 28 2015 brew-cask -> ../Cellar/brew-cask/0.58.0/bin/brew-cask