I have a 1 year old Cub Cadet lawn tractor that will start and stay running if I start it by priming the carburetor with a little gas. Fuel filter and fuel pump seem to be working. When I stop the tractor, basically it automatically turns the engine off when I get off the seat, it will not restart. The only way to get it running again is to do the same - put a little gas in the carburetor. What else should I check?

I'm not familiar with your mower (a) because it's probably too new compared to those I'm familiar with and (b) you haven't identified it besides saying it's a Cub Cadet. The next thing to check is whatever chokes or primes that engine. Some engines have a choke lever; others have an automatic choke; yet others have a primer bulb. Whatever it is that yours employs, check that it's working.
 
There are certainly other things that would make an engine hard to start, but since you mentioned that it's only a year old, I wouldn't yet pay attention to things like low compression or valve clearance. First rule out malfunction in the choke or prime, as your case may be.

+1 ^^..     We need the Make, HP and MODEL of the engine...
 
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