There's a killer script on github that fixes perms on /usr/local and brew directories to be accessible by anyone who is a member of the 'admin' group.
https://gist.github.com/jaibeee/9a4ea6aa9d428bc77925
This is a better solution than the chosen answer, since if you chown the /usr/local/___ directories to $USER, then you break any other admin users of homebrew on that machine.
Here are the guts of the script at the time I posted this:
chgrp -R admin /usr/local
chmod -R g+w /usr/local
chgrp -R admin /Library/Caches/Homebrew
chmod -R g+w /Library/Caches/Homebrew
chgrp -R admin /opt/homebrew-cask
chmod -R g+w /opt/homebrew-cask