It is possible to run Virtual Machines inside Virtual Machines (VMs). That is called Nested Virtualization. 
Running VirtualBox, KVM or Qubes inside Qubes is difficult. Not offically supported by the Qubes developers. It's unrelated to Whonix. You can learn more about the current state of things by searching the qubes-devel and qubes-users mailing lists for terms such as VirtualBox, KVM and/or nested virtualization.
VirtualBox inside VirtualBox
Be sure to change your host key. VirtualBox -> Preferences -> Input -> Host Key. The "outside" and the "inside" Host Key must differ, otherwise you can not leave the VM "inside" anymore.
VirtualBox does not support VT in VT yet.  So the "inside" VM might be slow depending on your host's performance. Inside the "inside" VM, disable VT. VirtualBox -> right click on VM -> Settings -> System -> Acceleration -> uncheck "Enable VT-x/AMD-V"
- VirtualBox -> right click on VM -> Settings -> System -> uncheck "Enable IO APIC"
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