apt-get -f install cannot unpack archive

Question

The error states it cannot unpack a file due to

No space left on device

However this is wrong - there is plenty of space. Here is the output...

root@myserver:/# apt-get -f install
Reading package lists... Done
Building dependency tree       
Reading state information... Done
Correcting dependencies... Done
The following packages were automatically installed and are no longer required:
  linux-cloud-tools-3.13.0-105 linux-cloud-tools-3.13.0-105-generic
  linux-cloud-tools-3.13.0-106 linux-cloud-tools-3.13.0-106-generic
  linux-cloud-tools-3.13.0-107 linux-cloud-tools-3.13.0-107-generic
  linux-cloud-tools-3.13.0-108 linux-cloud-tools-3.13.0-108-generic
  linux-cloud-tools-3.13.0-109 linux-cloud-tools-3.13.0-109-generic
  linux-cloud-tools-3.13.0-110 linux-cloud-tools-3.13.0-110-generic
  linux-cloud-tools-3.13.0-112 linux-cloud-tools-3.13.0-112-generic
  linux-headers-3.13.0-105 linux-headers-3.13.0-105-generic
  linux-headers-3.13.0-106 linux-headers-3.13.0-106-generic
  linux-headers-3.13.0-107 linux-headers-3.13.0-107-generic
  linux-headers-3.13.0-108 linux-headers-3.13.0-108-generic
  linux-headers-3.13.0-109 linux-headers-3.13.0-109-generic
  linux-headers-3.13.0-112 linux-headers-3.13.0-112-generic
  linux-headers-3.13.0-115 linux-headers-3.13.0-115-generic
  linux-image-3.13.0-105-generic linux-image-3.13.0-106-generic
  linux-image-3.13.0-107-generic linux-image-3.13.0-108-generic
  linux-image-3.13.0-109-generic linux-image-3.13.0-112-generic
  linux-image-3.13.0-115-generic linux-image-extra-3.13.0-105-generic
  linux-image-extra-3.13.0-106-generic linux-image-extra-3.13.0-107-generic
  linux-image-extra-3.13.0-108-generic linux-image-extra-3.13.0-109-generic
  linux-image-extra-3.13.0-112-generic linux-image-extra-3.13.0-115-generic
Use 'apt-get autoremove' to remove them.
The following extra packages will be installed:
  linux-image-3.13.0-115-generic linux-image-3.13.0-116-generic
Suggested packages:
  fdutils linux-doc-3.13.0 linux-source-3.13.0 linux-tools
The following NEW packages will be installed
  linux-image-3.13.0-115-generic linux-image-3.13.0-116-generic
0 to upgrade, 2 to newly install, 0 to remove and 55 not to upgrade.
17 not fully installed or removed.
Need to get 0 B/30.7 MB of archives.
After this operation, 86.6 MB of additional disk space will be used.
Do you want to continue? [Y/n] y
(Reading database ... 328184 files and directories currently installed.)
Preparing to unpack .../linux-image-3.13.0-116-generic_3.13.0-116.163_amd64.deb ...
Done.
Unpacking linux-image-3.13.0-116-generic (3.13.0-116.163) ...
dpkg: error processing archive /var/cache/apt/archives/linux-image-3.13.0-116-generic_3.13.0-116.163_amd64.deb (--unpack):
 cannot copy extracted data for './boot/abi-3.13.0-116-generic' to '/boot/abi-3.13.0-116-generic.dpkg-new': failed to write (No space left on device)
dpkg-deb: error: subprocess paste was killed by signal (Broken pipe)
Examining /etc/kernel/postrm.d .
run-parts: executing /etc/kernel/postrm.d/initramfs-tools 3.13.0-116-generic /boot/vmlinuz-3.13.0-116-generic
run-parts: executing /etc/kernel/postrm.d/zz-update-grub 3.13.0-116-generic /boot/vmlinuz-3.13.0-116-generic
Preparing to unpack .../linux-image-3.13.0-115-generic_3.13.0-115.162_amd64.deb ...
Done.
Unpacking linux-image-3.13.0-115-generic (3.13.0-115.162) ...
dpkg: error processing archive /var/cache/apt/archives/linux-image-3.13.0-115-generic_3.13.0-115.162_amd64.deb (--unpack):
 cannot copy extracted data for './boot/abi-3.13.0-115-generic' to '/boot/abi-3.13.0-115-generic.dpkg-new': failed to write (No space left on device)
dpkg-deb: error: subprocess paste was killed by signal (Broken pipe)
Examining /etc/kernel/postrm.d .
run-parts: executing /etc/kernel/postrm.d/initramfs-tools 3.13.0-115-generic /boot/vmlinuz-3.13.0-115-generic
run-parts: executing /etc/kernel/postrm.d/zz-update-grub 3.13.0-115-generic /boot/vmlinuz-3.13.0-115-generic
Errors were encountered while processing:
 /var/cache/apt/archives/linux-image-3.13.0-116-generic_3.13.0-116.163_amd64.deb
 /var/cache/apt/archives/linux-image-3.13.0-115-generic_3.13.0-115.162_amd64.deb
E: Sub-process /usr/bin/dpkg returned an error code (1)
root@myserver:/#

Also, if I do apt-get autoremove I get this...

root@irishjeweller:/# apt-get autoremove
Reading package lists... Done
Building dependency tree       
Reading state information... Done
You might want to run ‘apt-get -f install’ to correct these.
The following packages have unmet dependencies.
 linux-image-extra-3.13.0-115-generic : Depends: linux-image-3.13.0-115-generic but it is not installed
 linux-image-extra-3.13.0-116-generic : Depends: linux-image-3.13.0-116-generic but it is not installed
 linux-image-generic : Depends: linux-image-3.13.0-116-generic but it is not installed
E: Unmet dependencies. Try using -f.