I have installed Android Studio in Windows 2012 Server machine on Google Cloud. But, I cannot run Emulator on it. It shows the below error.
"HAXM doesn't support nested virtual machines"
Consider that nested virtualisation is not enabled out of the box for Compute Engine instances. Therefore you need to enable it manually, however it is not available yet for Windows instances as you can check in the documentation page:
Nested virtualization does not currently support Windows instances.