Can I install Windows 7 64 bit on VirtualBox running on a Windows 7 32 bit OS?

Solution 1:

VirtualBox versions 2.1+ support 64 bit guests inside 32 bit hosts, assuming the following is true:

  1. You need a 64-bit processor with hardware virtualization support (see chapter 1.2, Software vs. hardware virtualization (VT-x and AMD-V), page 11).
  2. You must enable hardware virtualization for the particular VM for which you want 64-bit support; software virtualization is not supported for 64-bit VMs.
  3. If you want to use 64-bit guest support on a 32-bit host operating system, you must also select a 64-bit operating system for the particular VM. Since supporting 64 bits on 32-bit hosts incurs additional overhead, VirtualBox only enables this support upon explicit request.

From. http://www.virtualbox.org/manual/ch03.html#intro-64bitguests

Hosting a Windows guest inside a Windows host shouldn't be a problem, so as long as you pass the three points, it should work.