From Wikipedia (Childhood):
Quentin was only four years old when his father became president, and he grew up in the White House. By far the favorite of all of President Roosevelt's children, Quentin was also the most rambunctious.
Quentin's behavior prompted his mother, Edith, to label him a "fine bad little boy." Amongst Quentin's many adventures with the "White House Gang" (a name assigned by T.R. to Quentin and his friends), Quentin carved a baseball diamond on the White House lawn without permission, defaced official presidential portraits in the White House with spitballs, threw snowballs from the White House's roof at unsuspecting Secret Service guards, and occasionally rode on top of the family elevator with his friend, Charlie Taft. Charlie, the son of Secretary of War and future President William Howard Taft, was also part of the White House Gang.
He quickly became known for his humorous and sometimes philosophical remarks. To a reporter trying to trap the boy into giving information about his father, Quentin admitted, "I see him occasionally, but I know nothing of his family life." The family soon learned to keep him quiet during dinner when important guests were present.
Once, when his brother Archie was terribly ill, it was Quentin (with the help of Charles Lee, a White House coachman), who brought the pony Algonquin to his room by elevator, sure that this would make his brother smile.
As a young man, Quentin displayed a natural mechanical aptitude. He could fix almost anything, and rebuilt a motorcycle to present to a friend as a gift.