This is possible, given that your motherboard and processor support CPU virtualization. From the VirtualBox manual:
VirtualBox supports 64-bit guest operating systems, even on 32-bit
host operating systems, provided that the following conditions are
You need a 64-bit processor with hardware virtualization support.
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
the particular VM. Since supporting 64 bits on 32-bit hosts incurs
additional overhead, VirtualBox only enables this support upon
I know this is also possible to do with VMWare. The underlying idea here is that, if you have a 64-bit processor which supports virtualization, it is possible since the virtual machine executes code directly on the CPU. I don't know if this will allow you to use the extra RAM in your system, but there are other things you can do with the extra memory.
If you extended the pagefile into the extra memory (using that previous link), you could theoretically recover some of the extra RAM (albeit with some overhead). Using that method, you would probably be better off using a 32-bit guest (to avoid the 64-bit RAM address overhead on a 32-bit OS).