Construction has begun on a sixstory shopping and office building complex on the site of the former Apex theater at 48th Street and Massachusetts Avenue NW in Spring Valley.

To be known as 4801 Massachusetts Avenue, the project of the Melvin Lenkin and Frederick Burka families was designed by architect Vlastimil Koubek to have two atriums inside 121,500 square feet of office space, 55,00 square feet of retail space and a three-story paking garage for 385 cars.

Aetna Life & Casualty announced that arrangements for $14.3 million in interim and permanent financing were made through the B.F. Saul Co., its mortgage loan correspondent here.

A spokesmen for the Burka family, which owned the former Apex theater, build in 1940, said the start of construction on the shopping center had been delayed for months by "legal problems that have been resolved." There hhad been neighborhood opposition to the new project.

Completion of the brick structure is scheduled late in 1980 by a construction firm headed by Melvin Lenkin.

Leasing is being handled by the Washington office of Julien J. Studley firm said that early begotiations are under way for leases with a branch bank, a savings and loan association, two realty offices and a "tablecloth restaurant."