Go to your MySteinberg/Downloads and download the full Cubase 8 installer (a 9 GB .iso file) - if you haven’t got it already. No need to install previous versions then.
Don’t know what you mean with ‘installer tool’ or ‘the core’ but you just have to make sure to download the latest eLicenser software and get your USB-key recognized. You valid license should be on it, or if you haven’t activated your C8 license you should do that first. Then install any version of Cubase you want; 8 or previous, or both/all.