When the city’s Education Department said it would not let students from the Beacon School on the Upper West Side take a spring break trip to Cuba this year, the school turned to a powerful friend for help: Lt. Gov. David A. Paterson, whose stepdaughter went on the trip as a Beacon student in 2005. His call did not make a difference; city officials would not budge.

But the students went anyway, chaperoned by one teacher and two parents. And yesterday, city officials, including Schools Chancellor Joel I. Klein and even Mayor Michael R. Bloomberg, were left struggling to explain why the trip went forward, and how Beacon students had managed to get to Havana again this year in defiance of the government’s ban on travel to the Communist nation.

Mr. Klein, at a news conference yesterday, said that the trip had not been approved by the Education Department and that the matter was now under investigation. “It should not have happened,” Mr. Klein said. “We expressly said no.”

Officials said yesterday that they had been unaware of the school’s previous trips to Cuba, in 2004 and 2005, prompting questions from Mr. Paterson.

“As a parent,” Mr. Paterson said by telephone, “I was a little concerned that a group of schoolchildren went to Cuba and the Department of Education didn’t know about it.”

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