I have a Cub Cadet 1500 series, model # 13A221F100. I bought new battery, replaced both cable terminals, replaced both spark plugs. My riding mower will start but it cuts off after a few seconds. Help.

Check for good grounding under the seat for a safety switch. If that ground is intermittent then it can shut off. That being said.

Also sounds like carb needs fuel.

Did you change fuel filter also?
Try carb cleaner and see if carb works better.

Fuel can be bad in tank. Always use New fuel when trouble starts like this. I drain tank and new High test fuel to start. Fuel can cause this also. I'm anal that way solved many what thought to be carb problems that way.
Is short.
Fuel filter.
Cracked fuel lines and or bad fuel clamps

Fuel pump in carb bad.
Float in carb stuck.

The best way to test the engine and take the carb out of the equation is I use a hand pump spray bottle with high test gas and spray in the carb and if I can keep the engine running its defiantly the carb fuel / fuel pump problem not the engine spark coil problem.

Try the aboves and get back so we can narrow this down more.

Remove gas cap, start mower, see what happens.

Check for good grounding under the seat for a safety switch. If that ground is intermittent then it can shut off. That being said.

Also sounds like carb needs fuel.

Did you change fuel filter also?
Try carb cleaner and see if carb works better.

Fuel can be bad in tank. Always use New fuel when trouble starts like this. I drain tank and new High test fuel to start. Fuel can cause this also. I'm anal that way solved many what thought to be carb problems that way.
Is short.
Fuel filter.
Cracked fuel lines and or bad fuel clamps

Fuel pump in carb bad.
Float in carb stuck.

The best way to test the engine and take the carb out of the equation is I use a hand pump spray bottle with high test gas and spray in the carb and if I can keep the engine running its defiantly the carb fuel / fuel pump problem not the engine spark coil problem.

Try the aboves and get back so we can narrow this down more.

I drained fuel tank, checked and drained fuel lines, checked the bowl and found orange colored residue and water looking fluid (stale fuel), and it starts right up. Thanks for quick response.