brew cask upgrade does not seem to work
There is no upgrade command available for brew cask. The GUI apps are updates by running Check for updates... from within the application which is generally found in the menu.

You can force install a newer version of the cask item by running brew cask reinstall &lt;package&gt;. In case of Google Chrome, run brew cask reinstall google-chrome.

You can use brew cask upgrade --greedy to upgrade all the GUI apps to respective latest version. From man brew-cask:


  upgrade [--force] [--greedy] token [ token ... ]
  
  Without token arguments, upgrade all the  installed  Casks  that
    have  newer  versions available in the tap; otherwise update the
    tokens given in the command line. If --greedy is given then also
    upgrade the Casks having auto_updates true or version :latest.