mght be that your fuel cap vent is stopped up. Loosen cap and run engine to test.
If prob still there, chk/replace all fuel lines from tank to carb. Also make sure that inline fuel filter ir oriented in correct direction.
Can also remove fuel line at crab and crank engine to verify fuel pump function. Use catch container and be careful. Should see a healthy stream of fuel. If not, repair fuel pump.
If flow good, but still prob, time to remove carb for a thorough cleaning,probed with stiff small dia copper wire, blown out with compressed air, rebuilt with new gaskets and valve seats - get rebuild kit from local Cub dealer.

repost back with results. Good luck

Yes, fuel cap vent would be nice and easy. Debris in the carb just floating at the bottom is another likely scenario. These you can buy the whole expensive carb kit, or the float valve and body gasket. A couple of things that are easy and fairly specific go back to the routing of the fuel line. Due to the mounting of the pump, it is easy to loop the line above the pump- which can vapor lock on these. AT least if I'm remembering right and this has the horizontal Vangard engine. Obviously the right fuel line, clamps filter should be used. Think too that if the line that travels to the fuel tank is getting spongy and weak, the pump can't do its job well. The pulse line to the pump must also be secure, things that lose a great deal of crankcase vacuum can affect pump operation.

My mother's older cub cadet started having fuel system problems after she started using fuel with ethanol. First, the rubber seal on the gas cap melted and wound up in the gas tank. After that was fixed, it wasn't long until the main fuel line failed about midway between tank and engine. Just a couple more things to look at.

I'd check the fuel filter as well.