Exhibit (32)(1)

CERTIFICATION PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

18 U.S.C. SECTION 1350

In connection with the Quarterly Report of C-COR Incorporated (the “Company”) on Form 10-Q for the period ending December 23, 2005 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, David A. Woodle, Chief Executive Officer of the Company, certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, 18 U.S.C. Section 1350 that, to my knowledge:

1. The Report fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

2. The information contained in the Report fairly presents, in all material respects, the financial condition and result of operations of the Company.

/s/    DAVID A. WOODLE        

David A. Woodle

Chief Executive Officer

February 1, 2006