America's Hispanic population expanded out of its traditional centers in the southwestern United States during the 1970s and grew rapidly in many parts of the country, including the Washington metropolitan area, the Census Bureau reported yesterday.

Mexican-Americans showed the greatest increase, surging by 93 percent in the decade to 8.7 million. The Mexican population in Illinois, Colorado, and Washington state more than doubled, the Census Bureau said, though by far the largest numerical gains--about 3 million combined--were in California and Texas.

Meanwhile, the number of Puerto Ricans living on the U.S. mainland climbed by 41 percent to just over 2 million. The percentage living in New York, their traditional port of entry, dropped from 64 percent in 1970 to 49 percent in 1980.

The country's Cuban population grew by 48 percent to 803,226. Almost three-fifths of them lived in Florida, the Census Bureau said, but sizeable Cuban populations also have developed in New Jersey and California.

Overall the number of Hispanics in the U.S., including those from Central and South America, reached 14.6 million in 1980--a 61 percent increase over the decade compared to just an 11 percent rise in the total U.S. population.

In 1980 some 6.4 percent of Americans were of Spanish origin, compared to 4.5 percent a decade earlier. Blacks, however, continued to be the country's largest minority group, increasing by 17 percent to 26.5 million or 11.7 percent of the total population. The number of Asians more than doubled during the decade to 3.5 million, or 3 percent of the U.S. total.

Census officials suggested that the sharp jump in Hispanics was caused by substantial immigration--both legal and illegal, as well as by a high birth rate and efforts to improve the census count.

"There's been growth in the traditional areas (of Hispanic settlement) but also a real dispersal of the Spanish population around the country," Census Bureau director Bruce K.Chapman said yesterday. "It's tremendous."

In the Washington metropolitan area the Hispanic population grew by 72.3 percent during the decade and reached 93,380 in 1980. It accounted for 3.1 percent of the area's total population, less than half the national average, but up sharply from its 1.9 percent share a decade earlier.

Virtually all the growth in Hispanics occurred in the suburbs, where the Spanish population went from 39,073 to 75,701. The District of Columbia's Spanish population, despite considerable visibility in the Adams-Morgan area, increased by just 2,57l to 17,679.

Of the area's Hispanics 66 percent are listed by the Census Bureau as "other Spanish." This means they came from Central or South America or did not give a specific country of origin. Around the country just 21 percent of the Hispanic population was in that category.

About 60 percent of the country's Hispanics were of Mexican origin, 13.8 percent Puerto Rican, and 5.5 percent from Cuba. In the Washington area Mexicans accounted for just 15 percent of the Hispanic group, Puerto Ricans for about 10 percent, and Cubans 8 percent.

According to the Census Bureau, 15 states now have more than 100,000 Hispanics, compared to 12 states with that many in 1970. The state of Washington has been one of the fastest gainers with its Spanish population rising in the decade from 57,358 to 120,016.

In the 1980 census there were more Hispanics than blacks in Washington and 14 other states, including California and Texas. Hispanics comprised 19.2 percent of the population of Texas and 21 percent of California, though New Mexico continued to have the country's highest proportion of Hispanics, 36.6 percent.

The Spanish population reached 64,746 in Maryland and 79,868 in Virginia in 1980 with gains over the decade of more than 50 percent. Hispanics accounted for 1.5 percent of each state's population.

In the census count, the number of Hispanics was based on self-identification in response to a question about Spanish "origin or descent" rather than a strict definition of language-use or place of birth.

Overall, the Census Bureau said 11.l million Americans speak Spanish at home, though three-quarters of them said they also spoke English well. In the Washington area 86,492 persons speak Spanish at home, the Census Bureau reported.