I would like to do some lib testing on my OS. So I need several environment to run KVM. And I found my guest machine was not able to run KVM.
I was using virtualbox 4.2.
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Therefore, KVM can't run in VirtualBox (yet). Please track bug ticket #4032.
VT-X and AMD-V (so-called virtualization extensions) run the guest operating system natively in the CPU. Without them, the virtualization software must interpret the operating system opcodes in software, which is very slow.
For now, you can either
Virtualbox just released (12/18/2018) version 6 in which is expected to have nested virtualization. However, at this moment it seems is still unavailable on Intel procs. https://www.virtualbox.org/wiki/Downloads
Regarding the main question (Enable nested virtualization in Ubuntu) - KVM module is supporting nested virtualization on Ubuntu 16 and above (maybe lower versions too). Not sure about using XEN on host, but you can nest XEN in KVM for sure.