The Reagan administration, which put out the lantern on the Statue of Liberty and closed down the Washington Monument to dramatize its horror at congressional extravagance, is about to squander $10 million on a special broadcasting station aimed at Cuba.

At its inception, the station was called "Radio Marti." Jose Marti was a Cuban intellectual, a hero at the time of the Spanish-American War, and is much cited by Fidel Castro. But somebody did a little belated research and found an embarrassing richness of anti-American quotations in Marti's work.

It was back to the drawing board on the name but not on the idea, which is to tell Cubans about Cuba.

What makes this plan so witless is that Cubans are addicted to U.S. commercial radio stations. They are mad about rock and demented about baseball. Three Spanish-language stations in Miami have enormous Cuban audiences, and other stations in the southern United States report tremendous responses to contests they promote on the air.

Cubans like everything about America except a government that has subjected them to 20 years of economic boycott and diplomatic isolation.

They can, if they want to hear the official view of Washington, listen to the Voice of America, which broadcasts to them regularly from Florida.

But this is not enough for administration spendthrifts.

In spite of Castro's warning that he will jam Radio Broadcasting to Cuba, Inc.--as Radio Marti has been renamed--and create several new stations in his country to compete with U.S. stations, the State Department is pressing ahead with its provocative plan.

At State's request, Sen. Charles H. Percy (R-Ill.), chairman of the Foreign Relations Committee, introduced a bill calling for establishment of the station to operate "in a manner not inconsistent with the broad foreign policy objectives of the U.S."

As to what this means, no one is quite sure. Frank Shakespeare, who was up for confirmation as chairman of the board of International Broadcasting, which will oversee the new station as it does the Iron Curtain broadcasts of Radio Free Europe and Radio Liberty, seemed vague about its purposes and goals.

When Sen. Larry Pressler (R-S.D.) artlessly inquired if the new station might lead to formation of a militantly anti-Soviet organization, such as Poland's Solidarity, Shakespeare backed off in haste.

Would the new broadcasting corporation attempt to foment revolution in Cuba? Would it incite Cubans to come to the United States? We cannot cope with the current tide of Cuban and Haitian refugees, many of them huddled in miserable camps that the station's $10 million cost could be better used to improve.

The new venture would be "a surrogate local radio service," said Shakespeare, who was head of the U.S. Information Service (now the International Communication Agency) in the Nixon administration. Cuban listeners could tell the difference between the Voice of America and the new station because the Voice would tell them about America, while "Inc." would tell them about Cuba. The question is would they believe it?

Whatever its goal, the new service probably should engage Alexander M. Haig Jr. as its Walter Cronkite. The secretary of state considers himself America's leading authority on the island, and hardly a day goes by that he does not uncover some new mischief being perpetrated by Fidel Castro.

Just this week from Mexico, Haig informed us from his own private sources that Soviet-made Mig fighters have arrived in Havana for eventual shipment to Nicaragua, a country against which, he hints constantly, he must take military action.

Maybe instead of making Haig a newscaster, we should drop the whole idea of Broadcasting to Cuba, Inc., and try another tack with Castro.

No less than a senior fellow at Ronald Reagan's favorite think tank, the Hoover Institution, argues in "Hoover Essays" for a U-turn in Cuban-American relations.

Writes Robert Wesson: "The cutting-off of diplomatic relations, the closure of the U.S. market, the halting of the once-vital tourist traffic, plus many a paramilitary pinprick, have had no success in either toppling the Castro government or making it less anti-American . . . and left Castro entirely dependent on Soviet support and to a large extent subservient to Soviet design."

Reopening trade with Cuba would save the Soviet Union, its sole support, about $3 million a day but, Wesson says, "a U.S.-Cuban rapprochement would have beneficial effects throughout Latin America, where Cuba's influence is primarily due to its open defiance of the U.S."

By lifting the embargo, the United States would save a lot more than the $10 million for the inane "Inc." With Cuba exporting goods to us instead of revolution to Latin American countries, we would not have to spend money on a blockade, one of the martial ideas that the secretary of state keeps floating by us.

Castro drives American presidents crazy because he is cheeky.

But somebody in this administration ought to look at the numbers and figure out he would be much less expensive a friend than an enemy.