One white child in eight under 18 - and two of five black children under 18 - live in families without a father present, according to a new Census Bureau profile of American children and youth.

These figures, about a third higher in each case than six years ago, help explain the high incidence of poverty among black children that is also revealed in the new census report. Families headed by a mother only, without the support of a father, tend to be among the poorest in the nation, filling the welfare rolls and living on charity in many cases.

The census figures show that in 1975, 12.5 percent of white children were in families below the poverty line, but for blacks it was 41.4 percent. Over two-thirds of the black poverty children were in family-headed families.

Families headed by women tend to be the main poverty families because fewer women than men work, their work is more sporadic and their pay is generally lower.

Nevertheless, the census report shows that between 1970 and 1976, the percentage of children under 13 whose mothers were working rose from about 39 percent to nearly 46 percent.

The report bears out earlier statistics indicating that the unemployment rates for young persons - particularly among minorities lacking education are extremely high. Among youths 16 to 24, not enrolled in school, an eighth of the whites, 27 percent of the blacks and 16 percent of those of his panic origin were unemployed in 1976.

Among non-high school graduates, the rates were staggering - about 22 percent for whites and Hispanics, but 37 percent for blacks. Even blacks who had a few years of college education but did not graduate had a very high rate - 27 per cent - which was substantially greater than whites or Hispanics. Only among those with four years of college or more was the black unemployment rate at the same level as that of white youths, 7.1 percent.

While these figures document severe economic disadvantage for black youth, there are some optimistic statistics in the census report as well.

Nursery school enrollment has jumped substantially and is now nearly 50 percent of all children age 3 to 5 among blacks and whites.

Among youths of 18 to 24, the percentage of high school graduates among blacks has jumped from 56 percent to 68 percent in six years. Whites have increased less but still have a higher proportion of high school graduates (81 percent). About a third of graduates in each race are enrolled in college, a big increase for blacks over the past decade.

The rise in black college enrollments has been particularly marked in the past decade. While white enrollments rose about 50 percent to 6.3 million, the number of black males in college nearly tripled (to 331,000) and the number of black females rose four-fold to 417,000.

As compared to men, the number of women of both races enrolled in college increased rapidly in the past decade. In 1970, there were 3 million men and 1.9 million women enrolled in college, and the ratio had narrowed to 3.7 million men and 3.5 women in 1976.

The census figures reveal some interesting changes in the types of programs undertaken by college students. In 1970, more people were studying to be teachers (1.1 million) than for any other field.

Business and commerce studies was second at 888,000. The health professions and biological sciences were several slots down the list at 602,000.

By 1974, however, business-commerce had jumped 55 percent to nearly 1.4 million, teaching was about the same as a decade before, but the health professions-biology jumped 87 percent to 1.1 million, virtually tied with teaching.