Many DIYers think that remote primers pushes the fuel into the carburetor which they are not design this way. They meant to remove air from the fuel chamber while pulling fuel into the carburetor.
Also many uses carburetor cleaners that are design to be used on these cubes. They have delicate internal check valves that can be destroyed the use of the carb cleaner with wire probing and use of compressed air (used very close) being a is a no no.
I have been cleaning these cubes for over 12 yrs now with about a 98% success rate. I strictly use an ultrasonic cleaner with soap and water. Usually the only ones that I have priming problems are the Zama cube with build in primers used on Stihl equipment. The only other cube that I have a problem with are the ready start (choke-less) designs where the enrichment valve wears out and they don't enrich.
As always we need the equipment numbers to even start to troubleshoot the problem remotely. We are not magical there beside the OP.
Also did the OP replace any of the cube gaskets and disphragms? Most usually need at least a new metering diaphragm.