Here is a previous question on Quora about it: Is it possible to install Virtual machine inside a virtual machine using virtual box? aka nesting of virtual machines!
Short answer: You can run 32-bit operating systems nested, but not 64.
Can run 32 bits, 64 can not run
Below is the excerpt from my book: VirtualBox at warp speed, Book
Nested virtualization is running VM inside a guest VM. This is a fun topic/project to think about and mostly people wonder why this is important or what purpose it serves.
Understanding if this is possible and why if not, helps us understand virtualization better. For VirtualBox itself the answer to this is “yes” for running 32-bit nested guests and “no” for 64-bit. VirtualBox does NOT have the code for running 64-bit VMs without CPU Extensions (AMD-V Intel VT-x). So the inner VM that is running on a host VM will not be able to support 64-bit. The parent/host (which is a guest VM) will not have the CPU extension feature. Supposedly VMware and Xen support soft coding the CPU extensions. And then there are possibilities of crossing virtualization technologies such as starting Xen inside VirtualBox, etc.
The Intel Haswell CPU has a new virtualization technology called Virtual Machine Control Structure (VMCS) Shadowing. VMCS shadowing accelerates nested virtualization allowing guests to run with minimal impact. VMCS may become mainstream once all virtualization technologies start to implement it. VMCS allows you to run multiple hypervisors on one CPU natively. If there is a need to create nested VMs (or many VMs), consider running container based VMs such as Linux Containers or OpenVZ. Containers should typically run inside another VM without any issues.
Below are some reasons to use nested virtualization.