There is a problem writing to the disk.
$ df
and check the disc usage.
here is an example of a new vps
Code:
root@ds12-ams-2gb:~# df
Filesystem 1K-blocks Used Available Use% Mounted on
udev 1014796 0 1014796 0% /dev
tmpfs 204820 16044 188776 8% /run
/dev/vda1 40593708 3052664 37524660 8% /
tmpfs 1024092 0 1024092 0% /dev/shm
tmpfs 5120 0 5120 0% /run/lock
tmpfs 1024092 0 1024092 0% /sys/fs/cgroup
tmpfs 204820 0 204820 0% /run/user/1001
tmpfs 204820 0 204820 0% /run/user/0
Have you been caching images and used up your disc allocation? If no you have some permission error but apt runs as root ...