If you have any submenu on your navigation but the publish website show the icon as a square.
Please check your website URL whether it is published with or without www.
For example. Your website is abcd.com
Publish with www.
But if you access your website without www. like abcd.com, all the icon will display as the square box.
Publish without www.
If you publish your website without www., your website will be displayed correctly when you reach the website like abcd.com
But if you reach the website with www., all the icon will display as the square box.