It is possible to run virtual machines (VMs) inside other VMs. That is called nested virtualization: 
Nested virtualization refers to virtualization that runs inside an already virtualized environment. In other words, it's the ability to run a hypervisor inside of a virtual machine (VM), which itself runs on a hypervisor.
With nested virtualization, you're effectively nesting a hypervisor within a hypervisor. The hypervisor running the main virtual machine is considered a level 0, or LO hypervisor, and the initial hypervisor running inside the virtual machine is referred to as a level 1 or L1 hypervisor. Further nested virtualization would result in a level 2 (L2) hypervisor inside the nested VM, then a level 3 (L3) hypervisor within that nested VM, and so forth.
Not all hypervisors and operating systems support nested virtualization. Hypervisors that do support nested virtualization include KVM and VMware ESXi hypervisors (called Nested ESXi). Nested ESXi also supports Hyper-V, Xen and KVM guest hypervisors as of ESXi version 6.0.
Running VirtualBox, KVM or Qubes inside Qubes is difficult and is not offically supported by the Qubes developers; this is unrelated to Whonix ™. To learn more about the current state of support, search the qubes-devel [archive] and qubes-users [archive] mailing lists for terms such as VirtualBox, KVM and/or nested virtualization.
VirtualBox inside VirtualBox
First change your host key:
Host Key. The "outside" and the "inside" Host Key must differ, otherwise you can not leave the "inside" VM anymore.
VirtualBox only partially supports VT-in-VT -- nested AMD-V is functional (although not feature complete), while nested VT-x for Intel CPUs is still a work-in-progress.  Therefore the "inside" VM might be slow depending on your host's make and performance. For Intel CPUs, in the "inside" VM, disable VT:
right-click on VM →
uncheck "Enable VT-x/AMD-V"
- https://www.webopedia.com/TERM/N/nested-virtualization.html [archive]
vboxmanage "Whonix-Workstation" modifyvm --acpi on
right-click on VM→
uncheck "Enable IO APIC"
vboxmanage "Whonix-Workstation" modifyvm --ioapic on
- https://www.virtualbox.org/ticket/4032 [archive]
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