Try to add this PPA manually with
cat <<EOF | sudo tee /etc/apt/sources.list.d/sublime.list
deb http://ppa.launchpad.net/webupd8team/sublime-text-3/ubuntu artful main
deb-src http://ppa.launchpad.net/webupd8team/sublime-text-3/ubuntu artful main
EOF
and add its GPG key with
sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys EEA14886
or
sudo gpg --keyserver pgpkeys.mit.edu --recv-key EEA14886
sudo gpg -a --export EEA14886 | sudo apt-key add -
sudo apt-get update
or (with your proxy address and its port in the command)
sudo apt-key adv --keyserver keyserver.ubuntu.com \
--keyserver-options http-proxy=http://proxy_address:proxy_port \
--recv-keys EEA14886
then
sudo apt-get update
and so on.
Note: this answer is based on these : first, second and third.
Update:
try to get and install the package manually
cd /tmp
wget http://ppa.launchpad.net/webupd8team/sublime-text-3/ubuntu/pool/main/s/sublime-text-installer/sublime-text-installer_3126-2~webupd8~1_all.deb
sudo apt-get install ./sublime-text-installer_3126-2~webupd8~1_all.deb