International Business Machines Corp., the largest computer manufacturer in the world, said today its 1980 profits totaled $3.56 billion, up 18 percent from 1979.

IBM said the increase was largely attributable to lower tax rates in 1980. Profits before taxes were up only 6.2 percent. Earnings per share rose to $6.10 from $5.16.

In the final quarter of the year, IBM said it earned $1.23 billion ($2.11 a share), up from $1.01 billion ($1.73) in the same three months of 1979.

Gross income in the quarter climbed 14 percent to $7.81 billion. For the year, gross income rose to $26.21 billion, an increase of 15 percent.

Last year marked a return to increased profits for IBM after an earnings decline of 3.2 percent in 1979. Of American companies, only Exxon Corp. and American Telephone and Telegraph Co. have ever earned more than IBM's $3.56 billion in a year.

The fourth-quarter drop in the tax rate, one of the primary factors in the high earnings performance, was primarily a result of U.S. legislation enacted in December that affected the tax treatment of pension costs relating to certain foreign operations.