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.
• On 64-bit hosts (which typically come with hardware virtualization support), 64-bit guest operating systems are always supported regardless of settings, so you can simply install a 64-bit operating system in the guest.
• Warning

  On any host, you should enable the I/O APIC for virtual machines that you intend to use in 64-bit mode. This is especially true for 64-bit Windows VMs. See Section 3.3.2, “”Advanced” tab”. In addition, for 64-bit Windows guests, you should make sure that the VM uses the Intel networking device, since there is no 64-bit driver support for the AMD PCNet card; see Section 6.1, “Virtual networking hardware”.

Source: 64 bit – Does VirtualBox run 64-bit guests on a 32-bit host? – Ask Ubuntu