What is the smallest file size Ubuntu VirtualBox image with a GUI?
Lubuntu 16.04 is probably best and needs 4 GB minimum
I asked a similar for the smallest footprint / fastest flavour of Ubuntu here: Is one distribution better for Virtualbox 5.1 inside Ubuntu 16.04? and the answer was Lubuntu.
I created my Lubuntu 16.04 Virtual Image at 7 GB:
With nothing of significance installed other than the base packages it's showing 3.9 GB used and 3.5 GB available:
So I would say the minimum you could get away with is 4 GB using Lubuntu 16.04.
That said, my Ubuntu Unity 16.04.5 LTS installation with reams of applications installed and 3 kernel chains only takes up 9.8 GB. Next time around I'll probably just go with this version and forgo the extra effort of learning new interfaces and applications such as File Manager and File Editor.
The smallest official (and on-topic here) Ubuntu flavour with a GUI is Lubuntu and the minimal disk size is 3GB and the minimum memory requirements are 512MB resulting in 3.5 GB for a VM. (theoretical minimum, anything more is better)