Exhibit 32.1

CERTIFICATION OF PRINCIPAL EXECUTIVE OFFICER PURSUANT TO

18 U.S.C. SECTION 1350

AS ADOPTED PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

I, John T. Chambers, President and Chief Executive Officer of Cisco Systems, Inc. (the “Company”), do hereby certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to my knowledge:

• the Quarterly Report on Form 10-Q of the Company for the quarter ended January 29, 2005, as filed with the Securities and Exchange Commission (the “Report”), fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

• the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: February 18, 2005

/s/    JOHN T. CHAMBERS

John T. Chambers

President and Chief Executive Officer

(Principal Executive Officer)