After Malia Obama went off to Harvard University last month, her father couldn’t hold back the tears.

Barack Obama described that moment on Monday in a speech for the Beau Biden Foundation for the Protection of Children, which was named for former Vice President Joseph R. Biden’s older son, who died of brain cancer in 2015.

The former president said some kind words about Beau and his parents, Joe and Jill Biden, before talking about the joys and sorrows of watching children grow up.

“For those of us who have daughters, it just happens fast,” Mr. Obama said in a video published by WDEL, a news outlet based in Wilmington, Del.