Best thing is to change the DNS on your router, so instead of contacting the windows or steam server, it will contact your cache. If it's not present on the cache, the cache will download it and forward it to the client. So speed will be the same as directly downloading it from the server (windows or steam).
The issue you might be facing is the same as me that I not sure if there is a walk around. You first need to have a computer to download it first time. I don't think you can force one game or update on the cache server directly.
Otherwise it would be perfect for me.
My other solution would be to have a temporary computer or virtual open to force the download/install but it would require the double quantity of space, one for that system and one for the cache...