I am setting up application whitelisting using Windows Firewall and part of that process is allowing Windows Update, but I cannot seem to find where the executable is located. This is for both Windows 8.1 and Windows 10.
Actually, Windows Update is an system service, not an application. When checking the service properties, you can see:
Windows Update services runs with the system process: svchost.exe and it is using ports: 80, 443.
By default, Windows Firewall will not block the Windows Update. If you want to control it, please allow the svchost.exe and ports: 80, 443.