A BE55 ON A VFR FLT TO SSC FLEW INTO IFR CONDITIONS.

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BE55 OFF CUB VFR TO CDN (20 MIN FLT). CUB IS UNDER CAG AIRSPACE (CLASS C). CONTACTED ATC AND REQUESTED 2500 FT AND VFR FLT FOLLOWING. SKY CONDITION AT CUB RPTED TO BE 2600 FT SCATTERED. TAKING OFF RWY 13 INSTRUCTED TO TURN N TO STAY CLR OF CLOUD BASES WERE LESS THAN RPTED AND REQUESTED 3000 FT TO STAY CLR OF CLOUDS. REQUEST APPROVED AND INSTRUCTED TO CONTACT SHAW APCH ON 125.40. SHAW APCH BUSY AND DID NOT INITIALLY RESPOND. FINALLY AFTER 3-4 MINS THEY RESPONDED WITH AN ALTIMETER SETTING AND SQUAWK CODE. CALLED BACK AND INFORMED ATC THAT IT WAS BECOMING INCREASINGLY DIFFICULT TO MAINTAIN VFR AND TOLD TO CONTACT SHAW CLRNC ON 133.25. INFORMED SHAW CLRNC THAT IT WAS DIFFICULT MAINTAINING VFR. I TOLD SHAW CLRNC THAT I PLANNED TO DO THE NDB 24 APCH AT CDN AND THAT THERE APPEARED TO BE AN OVCST LAYER. AFTER PASSING THE NDB ON THE OUTBOUND COURSE; I WAS CLRED FOR THE NDB APCH AND INSTRUCTED TO MAINTAIN VFR. I INFORMED ATC THAT I WOULD BE ENTERING THE CLOUDS AT 2000 FT. ATC TURNED ME BACK OVER TO APCH CTL AND CLRED FOR THE VISUAL. INFORMED APCH THAT I WAS NOW PROC TURN INBOUND AND IMC. ASKED BY ATC IF I WOULD LIKE AN IFR CLRNC AND RESPONDED YES BUT THEN TOLD TO 'STAND BY.' AFTER ANOTHER MIN; ATC CAME BACK ON FREQ AS WE WERE BREAKING OUT OF THE CLOUDS AND HAD THE RWY IN SIGHT. WE CANCELED AND THE LNDG WAS UNEVENTFUL.