My mower wouldn't start so we started with the battery, that is fine so we checked the solenoid and replaced it, next the spark plug and when removing it there was gas in the hole that poured out. Changed the spark plug, checked the starter and that was fine, replaced the battery cable from the starter to the solenoid, still nothing so we brigded the solenoid and it fired up, blowing thick white smoke, ran for 15 sec. then died. I checked the oil to see if there was too much and found that there was gas in the oil.
Is this carberator or head gasket?

Carb not head issue. Your carb needle valve may be sticking or the float is stuck or saturated. Change the oil, open the carb bowl and check for float operation. The float should stop all fuel flow when raised, does it

I agree with Bob ,
You might check your needle and seat , alcohol in the gas now days is eating the rubber seats ,or the tip of the needle , not letting it seat tight , and flooding the carb.