A PIAGGIO 180 FLT CREW RPTED THAT THEY INADVERTENTLY ENTERED EWR'S CLASS B AIRSPACE AFTER DEP TEB.

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WE DEPARTED RWY 6 AT THE TEB ARPT ENRTE TO CDW; VFR NIGHT. PRIOR TO DEP I CALLED VIA TELEPHONE; THE TEB TWR AND ASKED IF I WOULD BE ABLE TO FLY THE 20 MILE FLT IN VFR CONDITIONS AND REMAIN CLEAR OF THE CLASS B AIRSPACE. THE TWR TOLD ME I COULD AND SAID TO CONTACT THEM ON GND CTL WHEN WE WERE READY TO GO. AFTER STARTING BOTH ENGS; MY FO CONTACTED GND CTL AND ASKED FOR CLRNC TO THE CDW ARPT IN VFR. HE TOLD US THAT WE WERE CLEAR TO DEPART TO THE WEST AND TO SQUAWK VFR. MY FO SPECIFICALLY ASKED FOR A DEP CTL FREQ AND HE STATED THAT WE DID NOT NEED ONE. I AGAIN ASKED IF WE WOULD REMAIN CLR OF THE CLASS B AIRSPACE AND HE RESPONDED; 'YES.' WE DEPARTED RWY 6; AND; WHEN APCHING 1000 FT MSL; I TURNED TO APPROX 250 DEGS DIRECT TO CDW WHILE CONTINUING TO CLB THRU 1700 FT MSL. AT THIS TIME TWR ADVISED US TO CONTACT NEW YORK APCH; HE WOULD LIKE TO TALK TO US AND WE DID. NY APCH ADVISED US THAT WE WERE IN THE CLASS B AIRSPACE BY APPROX 500 FT MSL. WE APOLOGIZED TO HIM. HE ACCEPTED OUR APOLOGY AND TOLD US TO BE MORE CAREFUL NEXT TIME. SUPPLEMENTAL INFO FROM ACN 604566: I WAS FLYING CO PLT IN A PIAGGIO P180 AVANTI TURBOPROP. WE WERE FLYING THE ACFT WITHOUT PAX FROM KTEB TO KCDW. THE PIC CALLED TWR ON THE PHONE PRIOR TO ENG START AND ASKED IF VFR WAS OKAY AND IF THERE WERE ANY AIRSPACE PROBS; OR IF HE RECOMMENDED IFR INSTEAD OF VFR. PIC WAS INFORMED THERE WERE NO CONFLICTS AND VFR WAS FINE. DURING TAXI; WE AGAIN ASKED THE KTEB ATC VIA RADIO IF WE SHOULD CONTACT NY APCH OR GET FLT FOLLOWING. WE WERE AGAIN INFORMED THERE WERE NO AIRSPACE CONFLICTS AND DUE TO SHORT DISTANCE (10 NM BETWEEN KTEB AND KCDW) THAT THERE WAS NO NEED TO CONTACT NY APCH. WE TOOK OFF AND CLBED TO 2500 FT MSL. KTEB TWR INFORMED US WE WERE INSIDE THE CLASS B AIRSPACE AND NY APCH WANTED TO TALK TO US VIA RADIO. WE CONTACTED THEM AND WERE INFORMED WE WERE 400 FT INSIDE THE CLASS B. WE DSNDED TO 1500 FT MSL; WERE GIVEN A TFC ADVISORY; AND SWITCHED TO KCDW TWR. LANDED AT KCDW. NY APCH INDICATED THAT NO FURTHER ACTION WOULD BE TAKEN ON THEIR PART. LESSON LEARNED: CHECK THE CHARTS BETTER AND FILE IFR IF VFR CLASS B OR SECTIONAL CHARTS ARE NOT AVAILABLE.