I have a 54 unit apartment building. Individual apartments are wired with CAT 6 back to the utility closet. From the utility closet I want to distribute a 7 mb DSL signal to/across these 27 apartments. Can I accomplish this with one router attached to a (or combination) 27 port switch or do I need a 27 port router?
BIG problems here. First, let's clarify something here, routers are not switches. What you'll want is a single router (something like a business-class Cisco router) and a 24 port switch along with another, smaller switch (because you have 27 customers). You need the business-class equipment because the amount of bandwidth that you'll be pushing through these switches/this router will be very large and you'll need good, reliable hardware to keep up with the demand.
Here's the BIG problem though, you're splitting a 7mbps connection to 27 residential customers. With this level of service you'd might as well not even have the connection at all. You SERIOUSLY need to invest in some sort of business class broadband (note that I said BUSINESS class) in order to provide the service you need. Residential class broadband would not be enough as the upload bandwidth is usually limited to around 1Mbps in most cable applications. Business class applications have much more upload throughput and the download bandwidth to match.
Your other option is to run a DSL line to EACH apartment individually. This is very expensive and would be no cheaper than the option I'm about to explain below.
Another problem: Security. The other reason you'll want to get business class hardware is because of the very large and very real security concerns that networking an entire apartment building entails. Unmanaged residential hardware simply does not have the software/hardware capability to isolate traffic and keep it tight. VLANs, Subnetting, etc are things that you will need to implement in order to get this thing running, features almost exclusively found on business hardware.
The moral of this story is: Don't be cheap. Hire a consultant, get some bids from local IT firms and do it right. If you do it yourself you're going to get burned because your tenants will start getting their own service anyways (because it's so slow) and you'll be out about $2000 with a network that is effectively useless. Or worse, they may even move out if you force them into this network.
Just trying to help. I'm a network tech by trade so this kind of thing is my life. I hope this gets you going in the direction you need. I wish you luck!