Can not upgrade Kali,not enough space in /var/cache/apt/archives

As you surmised, the issue is simply that you don't have enough space in your VirtualBox instance.

This line says it all:

/dev/mapper/kali--vg-root   12G   11G  250M  98% /

So you only have 250 MB of vacant space. And as apt is helpfully telling you:

After this operation, 622 MB of additional disk space will be used.

The solution is simple. Just extend the Logical Volume (LV) that your Virtualbox instance is living on. lvextend should do it. man lvextend should give you sufficient information. Ask on the site or in chat if you need more help.

Backup the virual machine ( clone it) then resize the virtual hard drive:

To incrase the kali.vdi from ~10 G to ~20 G use the following command (from Ubuntu):

VBoxManage modifyhd /Path/to/kali.vdi --resize 20000

Then download Gparted or use a linux live USB.

From Virtualbox, navigate to Setting > Storage > Controller IDE , then attach the gparted.iso

Configure the Virtual-Machine to boot from the optical drive (under Settings > System > Motherboard)

The virtual machine will boot into Gparted, you will be able to resize the virtual hard drive (10 ~> 20 G), apply changes , exit (shutdown)

Remove the attached gpartd.iso from the Controller IDE, then boot your virtual machine.