Symptom:

You have a Windows 7 virtual machine that cannot:

1. Do an initial round of Windows Updates after it is created (even with Internet access)

1. Install vmware tools

1. Windows Update error 80072efe
   

Note: the virtual machine in this instance was Windows 7 Pro Service Pack 1 x64

Resolution:

Download & install the following updates manually (onto the VM):

1. April 2015 Servicing Stack update (KB3020369) https://support.microsoft.com/en-us/topic/april-2015-servicing-stack-update-for-windows-7-and-windows-server-2008-r2-437ee749-51e0-6265-be9e-73fbd115d315
2. Convenience Rollup (KB3125574) https://www.catalog.update.microsoft.com/search.aspx?q=kb3125574
3. After the convenience rollup you’ll be asked to restart your computer
4. Reboot and run Windows Updates. All updates should now pull down to your virtual machine and complete successfully.