AN ATX FLC FLIES RWY HDG AFTER TKOF ROM CUB; SC. THEY SHOULD HAVE TURNED TO A 182 DEG HDG IN COMPLIANCE WITH THE PUBLISHED DEP PROC.

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DEPARTING CUB AT NIGHT; VISUAL CONDITIONS; IFR CLRNC OBTAINED BY REMOTE FREQ ON THE GND. PART OF THE CLRNC INCLUDED THE STATEMENT BY ATC TO 'FLY PUBLISHED DEP PROC;' WHICH IS TO TURN TO A HDG OF 182 DEGS AND CLB TO 2000 FT AFTER DEP. HOWEVER; THE CLRNC ALSO INCLUDED AN INSTRUCTION TO CLB TO 3000 FT. WITH MY COPLT TALKING ON THE RADIO AFTER TKOF; I WAS UNABLE TO MAKE MYSELF HEARD BY HIM UNTIL REPEATING 3 TIMES 'LEAVE UNICOM AND TALK TO DEP RIGHT AWAY;' AS WE DEPARTED 300 FT TO 400 FT AGL. HE WAS MORE INTENT ON LISTENING AND COMMUNICATING WITH CTAF FREQ TFC WHILE I WAS INTENT ON COMMUNICATING WITH ATC TO FIND OUT WHICH WAY THEY WANTED US HEADED IN THE ABSENCE OF A HDG IN THE CLRNC. WHEN ATC FINALLY CAME OVER TO US IN THE AIR PASSING THROUGH 1200 FT; HE WANTED TO KNOW IF WE WERE NOW ON A SOUTHERLY HDG. MY COPLT'S REPLY WAS 'NEGATIVE; 310 DEGS;' WHICH WAS RWY HDG. THE CTLR SAID HE HAD A TFC CONFLICT ALARM GO OFF AND THAT WE HAD ADDITIONAL TFC AT 1200 FT. NO DIRECTION RELATIVE TO US WAS GIVEN BY HIM; NOR DID WE SEE ANY ACFT LIGHTS OUTSIDE. WE CONTINUED OUTBOUND WITH ATC VECTORS FROM THERE ON. FAILURE TO REVIEW AND FLY PUBLISHED DEP PROC FROM RWY 31 AT CUB AND ACCEPT CLRNC DESPITE INITIAL RESERVATIONS.