Chemical New York Corp. and Marine Midland Banks Inc., two of the nation's largest banking corporations, said today that second-quarter profits increased substantially.

Chemical, whose primary subsidiary is Chemical Bank here, the nation's sixth-largest, listed a gain of 25.6 percent from the year-earlier period, largely on gains from high interest rates. Net income was $46.4 million ($2.98 a share), compared with $37 million ($2.35) a year ago.

The bank gained $256.9 million in net interest income -- the difference between interest earned on loans and that paid out on deposits and borrowings. That represents a 20.7 percent increase from net interest income of $212.9 million in the same period last year. For the first quarter of 1980, Chemical had a 6 percent profit gain.

Private analysts had predicted banks would record large profit gains for the April-to-June period, and such regional banks as American Security and Riggs National of Washington already have posted sharp gains. Analysts point to the unusually wide gap between the interest rates banks are charging their customers and the fees they pay to acquire their funds.

Chemical said its income for the first six months of the year rose 16.7 percent of $79 million from 67.7 million in the first half of 1979.

Among other large banks reporting second-quarter earnings today, Marine Midland Bank, the country's 13th-largest, posted a 37.2 percent increase over the year-earlier period. Its profits for the April-to-June period totaled $17.5 million ($1.11 a share), compared with $9.5 million (76 cents) in the second quarter last year. Marine Midland's net interest income rose 27.7 percent, to $105.7 million from $82.8 million.

Raytheon Co., a major electronics firm, today reported a 15.5 percent gain in second-quarter profits with an 11.7 percent rise in sales. Net income was $72.4 million ($1.75 a share) on sales of $1.25 billion, up from $62.7 million ($1.52) a year ago on sales of $1.12 billion.

First-half earnings were $137.6 million ($3.32) on sales of $2.45 billion, compared with $116.8 million ($2.83) on sales of $2.17 billion. The 1979 results are restated to reflect pro forma the acquisition of Beech Aircraft Co.

Government electronic systems and aircraft produced the biggest gains, the company said, but sales of Amana Radaranges and microwave ovens were well ahead of last year's pace. The order backlog climbed during the half to $5.30 billion from $4.76 billion a year earlier.

Metro-Goldwyn-Mayer Film Co. reported net income for the third quarter ended May 31 of $1.8 million (6 cents a share) on revenues of $39.2 million. The operations of MGM were divided May 30 into two publicly held corporations, MGM Filmco and MGM Grand Hotels Inc. Filmco had net income of $2.5 million (7 cents) on revenues of $46 million in the quarter ending May 31, 1979.

MGM Filmco had nine months earnings of $10.2 million (32 cents) on revenues of $130.9 million, compared to net income of $24.3 million (75 cents) on revenues of $154.6 million in the first nine months of 1979.

Kaiser Aluminum and Chemical Corp. reported earnings of 82.2 million ($1.98 a share) for the second quarter of 1980, compared with $59.6 million ($1.46) for the same period in 1979. Sales for the quarter were $939 million, compared with $803.3 million for the same quarter last year.