Martin Marietta Corp. yesterday reported a 25 percent increase in its second-quarter profits, with earnings rising to $71.6 million ($1.31 a share) from $57.3 million ($1.04) in the same time period a year ago.

Sales rose 12 percent, to $1.4 billion from $1.2 billion.

For the first six months of the year, Martin Marietta's earnings totaled $115.6 million ($2.11), up 9.4 percent from last year's $105.7 million ($1.92). Revenue for the six months was $2.5 billion, compared with $2.3 billion in the year-ago period.

"With strong contributions from all major business areas, earnings to date continue to track our expectations, and the growth in backlog to approximately $8.8 billion bodes well for the future," Martin Marietta's chairman, Thomas G. Pownall, said. The $8.8 backlog represented a 2 percent increase from the end of 1986 when the company's backlog was $8.6 billion. Alex. Brown Inc. reported a 25 percent increase in second-quarter profits to $7.3 million (44 cents) from $5.8 million (39 cents) for the same period in 1986. Revenue for the quarter increased by 37 percent to $85.6 million from $62.4 million.

For the first six months of the year, Alex. Brown's earnings were $15.2 million (94 cents), up 23 percent from $12.4 million (83 cents). Revenue for the first half of the year was $164.4 million, up 32 percent from $124.3 million.

"Obviously we are extremely pleased with the company's performance in the second quarter and year to date," said President Donald B. Hebb Jr. "However, we remain aware of the inherent volatility of the securities industry and do not consider the result of this quarter to be indicative of results for any future quarter." Legg Mason Inc., a Baltimore-based securities broker, reported a 13 percent decline in net income for the first quarter ending June 30.

Net earnings were $2.4 million (27 cents) compared with $2.8 million (40 cents) for the same period last year. The number of outstanding shares was 9.9 million this year compared with 6.9 million last year

Revenue for the quarter increased to $52.4 million from $34.3 million the previous year. The results include three recent acquisitions: Howard Weil Financial Corp., Western Asset Management Co., and Warren W. York & Co. Inc.

Earnings for the quarter were reduced by losses on municipal bond positions following rapid increases in interest rates in April and May, the company stated. CFS Financial Corp., the holding company for Continental Federal Savings Bank, announced a 35 percent increase in its earnings for the fiscal year that ended June 30.

Profits for the year were $5.4 million ($1.79) compared with $4 million ($1.73) the previous year.

For its last quarter, profits were up 76 percent to $948,000 (32 cents) from $538,000 (20 cents).