The Soviet Union recently installed big eavesdropping antennas in Cuba to intercept messages between the United States and overseas points, it was learned yesterday.

Administration officials confirmed that the new installation was located outside of Havana and already operational.

They conceded the "farm" of antennas represents a significant increase in Soviet monitoring of U.S. telephone calls, teletyped messages and computer talk but said coded military communications remain secure.

The primary purpose of the new eavesdropping facility, sources said is to intercept the hundreds of thousands of messages that are beamed in and out of the United States by statelite.

The eavesdropping antennas are targeted on the wide beam of messages that fly across the Atlantic via the three commercial communications satellities in space 22,300 miles above the ocean.

These Atlantic Ocean satellites, called Intelsat, connect the United States with 53 overseas nations, according to the Communications Satellite Corp., which lesses the circuits on them to international customers.

This intensified Soviet interest in commerical communications - such as messages about the future prices of grain and other commodities as well as investment of capital - signifies a deeper concern about economic trends worldwide.

The Soviet Union, sources said, will be picking up the traffic between the Intelsat satellites and ground stations located in Etam, W. Va., and Andover, Maine. But unlike those U.S. ground antennas which send as well as receive, the Soviet eavesdroppers in Cuba are only listening.

Presumably the Soviets will run the intercepted messages through a system of computers to sift out the information of prime interest. But this will not be easy.

A spokesman at the American Telephone and Telegraph Co. said that about 50,000 telephone calls travel through the three Atlantic satellites every business day. There are also thousands of teletype data messages going over the Atlantic via the satellites. The data are bursts of signals from one computer to another, such as prices in international trading centers.

Many businesses code their international emssages to keep competitors from intercepting commercial secrets. The disclosure that the Societ Union has installed sophisticated eavesdropping equipment in Cuba may increase the incoding of commercial traffic.

At the Communications Satellite Corp. headquarters in Washington, Sid Metzger, assistant vice president and chief scientist, said "customers have never been told communications are secure" and that sensitive information therefore should be scrambled or coded with devices on the market.

Metzger said receivers in Cuba could intercept the global beam going from U.S. ground stations to Intelsat satellites because that beam is so wide. But he said an eavesdropping station in Cuba would miss the outgoing narrower "spot" beams such as those from the United States to Europe.

A Cuban station, however, could intercept the incoming spot beam messages as they came down from Intelsat toward West Virginia and Maine, he said. The eaversdroppers would get only half the overseas communication - the down-link.

he Communication Satellite Corp. scientist theorized that Cuban-based receivers might be targeted on three other satellites now handling communications traffic between points in the United States.

Those three other satellites are Comstar leased by the Communications Satellite Corp. to AT and T and General Telephone and Electronics; Satcom owned by Radio Corp. of America, and Weststar, Western Union's satellite.

Carter administration officials have acknowledged that the Soviet Union has been intercepting U.S. telephone calls but have said sensitive military and diplomatic communications are adequately protected.

Said President Carter at his July 12 press conference: "Because of the radio transmission of telephone conversations, the intercept on a passive basis of these kinds of transmissions has become a common ability for nations to pursue. It's not an act of aggression or war . . ."

The United States, as well as other major powers, engages in widespread eavesdropping. U.S. eavesdropping on Russia from land stations, satellites and submarines makes it difficult to protest too loudly about the Soviets doing the same thing.

Sen. Daniel Patrick Moynihan (D-N.Y.) has lambasted the Carter administration for tolerating Soviet intercepts, contending they violate the constitutional rights of American citzens.

"We are letting the Russians treat us as if we were Russians," Moynihan said at a Senate intelligence subcommittee hearing on July 21. "We are doing it out of a fear of offending the principles of detente."

Responded Sen. Birch Bayh (D-Ind.): "We are very close to the old adage of he who lives in a glass house as how we address ourselves to this problem."