Total Possible Amperage of Sub-Breaker Box
40 Amps.  I've never heard those called &quot;cheater&quot; before - I think space saving is the term I've heard.
The total amps of all breakers in a panel often exceed the overall rating of the main breaker in the panel.  The reality is that not all circuits are pulling anywhere close to 100% of their rating 100% of the time.  Yes you can trip the main breaker.
The electrical service 125 Amps in your case is sized based on various factors.  It isn't sized based on the breakers (though the breakers would be associated with the applicances/devices used to size the service).  Here is an example online calculator that can help size the service.
http://www.douglashelmer.com/calculators/electrical/residential-service/index.htm