Unable to upgrade wordpress 3.6

If you get the following error:

Downloading update from http://wordpress.org/wordpress-3.6-new-bundled.zip…
Unpacking the update…
Could not create directory.: /var/www/wordpress/wp-content/upgrade/wordpress-3.tmp

Check that you have permissions to the /var/www/wordpress/wp-content/upgrade/ directory:

cd /var/www/wordpress/wp-content/
chown -R www-data upgrade
chgrp -R www-data upgrade