If you're running 32-bit Windows 7 on a 64-bit processor, then VirtualBox can run a 64-bit guest with a few caveats:
3.1.2. 64-bit guests
VirtualBox supports 64-bit guest operating systems, even on 32-bit host operating systems, provided that the following conditions are met:
You need a 64-bit processor with hardware virtualization support (see Section 10.3, “Hardware vs. software virtualization”).
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.
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.
To check whether your processor supports virtualization from Windows hosts, use the Microsoft Hardware-Assisted Virtualization Tool.
To check whether your processor supports virtualization from Linux hosts, run:
egrep '(vmx|svm)' /proc/cpuinfo
The above checks for either
/etc/cpuinfo. If it finds either, it prints out all of the flags. However, if it doesn't find them, it will not print anything. The latter means you do not have hardware virtualization.