You can delete the cache both automatically, manually.
If you have a permission problem with /wp-content/cache/ folder, you get the warning above.
1. Set the permissions of the following folders as below
2. Set the owner of the following folders as below
If you are still getting the permission warning although you have changed the permissions as above, you have a problem with the owner of the folders. As you see on the image below, the owner of the /all/ is different from others.
You need to set the owner of the folder with your username via terminal as below if you have dedicated server or VPS.
sudo chown -R USERNAME:USERNAME /YOUR_WORDPRESS_INSTALLED_PATH/
Note: If you have a hosting package, you cannot set the owner. In this case, you need to contact to your hosting provider.