Cosby C. Roberts, 56, president of Musicast Inc., a company that broadcasts background music to clients, including restaurants and offices, died Tuesday at George Washington University Hospital. He had diabetes.

Musicast has its headquarters in Clinton. In addition to broadcasting to clients, it leases speakers. From 1957 to 1962, Mr. Roberts had been vice president of WMAL Musicast and Michaels Enterprises. During those years, Musicast was broadcast from the WMAL tower. In 1962, Michaels Enterprises, which makes game machines and juke boxes, was sold and Mr. Roberts became president of the new Musicast Co.

Mr. Roberts was born in Washington and was a graduate of Eastern High School. He served with the Marine Corps in the Pacific during World War II. Following the war, he was a salesman with the Address-O-Graph Multigraph Co. until 1957.

He was a resident of Silver Spring and a member of St. Camillus Parish there. He was a past president of the Regina High School Home and School Association and had served on the school's board of directors. He also was a member of the International Rotary Club of Washington.

Survivors include his wife, the former Rose Marie Veneziani of Silver Spring; three daughters, Denise Roberts Brant of Chevy Chase, and Tina Angelica and Rina Elizabeth Roberts, both of Silver Spring; his mother, Ida Roberts of Ormand, Fla., and two sisters, Nellie Brinkley of McLean, and Alma Bushdid of Ormand.

The family suggests that expressions of sympathy be in the form of contributions to the American Diabetes Association, 4405 East-West Highway, Chevy Chase, Md.