Summary

If you are having the following error on your Gentoo system:

 Can't open the database file '/var/cache/eix/portage.eix' for writing (mode = 'wb')

Don’t waste your time, simply the /var/cache/eix directory is not present and/or writeable by the eix/portage use

mkdir -p /var/cache/eix
chmod +w /var/cache/eix*

Basic story is that eix will drop privileges to portage user when ran as root.