Reprinted from yesterday's late editions.

At the White House the other night, President Kenneth Kaunda of Zambia unabashedly borrowed a 12-string guitar from an entertainer and sang a freedom song he had written 24 years ago when he was leading his country's struggle for independence.

A few minutes later at the informal working dinner, the inevitable question of Cuban presence in Africa came up. Kaunda quickly flashed a Carter-bright smile and expalined that his past out-spokenness had ruffled some White House ears, but he went on anyway to say that the Cuban are in Africa "by invitation."

It was another example of the candor Kaunda has displayed during the three-day Washington portion of his eight-day visit to the United States.

"He has a tremendous influence on President Carter and Secretary Cyrus Vance," said U.N. Ambassador Andrew Young, standing a few feet away from Kaunda at a Zambian Embassy reception at the Washington Hilton Thursday. "He is credible, and his is the clear African perspective, and that's communicated every time he speaks."

Nearby, Richard Moose, assistant secretary of state for African affairs, echoed Young's appraisal. "He's a man who has a reputation for total integrity. He believes very deeply that morality should guide the decisions of government."

Earlier, at a luncheon at the National Press Club, a meatless one in honor of the president's dietary practices, Kaunda's rumbling voice was never raised as he talked of Africa's conflicts."Apartheid is a time bomb . . . the final explosion is not far behind," he said, his eyes surveying the capacity audience. "Now there is only an armed peace for southern Africa."

At Thursday's reception, Kaunda greeted the 800 guests on a receiving line, walked through the crowd briefly and listened to a New York African dancer and drummer troupe. "I love his smile; it's gentle and warm," said Egyptian Ambassador Ashraf A. Ghorbal. Ghorbal, who met with Kaunda Wednesday, disagrees with him on the Cuban presence in Africa. "Africa is out backyard, and we prefer outsiders to leave Africa alone," he said as he turned to join the ambassadors from the Soviet Union, Turkey and Lebanon. Most of the African ambassadors also were present Thursday.