Can I run virtualbox 64bit OS in a Azure Virtual Machine?

With a few exceptions, such as classic VMware on the guest, it's not possible to nest virtualization within virtualization. Although this would be a convenience for you, you'll have to attack it from another angle. Perhaps look into exporting a machine image from Virtualbox and then importing to Azure.

However, I did find somebody doing just what you ask: https://therightjoin.wordpress.com/2014/08/01/run-virtualbox-on-an-azure-virtual-machine/

This may work for 32-bit versions of guests, since those version do not require the hardware virtualization to be enabled (VT-d). I doubt you'll have any success with 64-bit guests.

For those like me, landing here from a search, this has changed: you can do nested virtualization with the new Dv3/Ev3 VMs: https://azure.microsoft.com/en-us/blog/nested-virtualization-in-azure/