Read. The. Post, people! This is not about a failed Schrader core. And it’s certainly not about two failed Schrader cores. The important bit you seem to be missing is “…after a few seconds it lost all its air through the valve.” Simeon Hope only thinks the air is coming out of the valve. Air escaping from a stem cut can often feel like it is coming out of the valve but it is coming out of the rim at the valve hole. It is not due to a poor quality tube nor to a loose valve.
Blaming the core is the reddest of red herrings.
Simeon Hope: inspect your tube. Pull the stem to one side and you’ll see a cut in the rubber around the stem. Alternatively, pump up the tube outside of the tire and feel for where the air is coming from. It will be immediately apparent.
As to the “why”, there are some different causes as I detailed in post 9 above.