I have a 15 inch down firing subwoof i plan on using over a cement floor purely for music, i have 18 inches of space to work in what should the dimensions of my cabinent be to get the best sound out of it?
I don't understand your post at all. If the woofer is down firing, I have to assume it is already in some type of cabinet. There is nothing unique about a driver that makes it "down firing". If it is not in a cabinet, then the cabinet volume and porting, if required, are going to be determined by the Thiel/Small parameters of the woofer.
So if it is a cabinet you want to build for that driver, it is impossible to help you without knowing the T/S parameters of your driver. I have to tell you the enclosure size will be dictated by the driver parameters and NOT your space limitations.