EXHIBIT 32.1

                    CERTIFICATION OF CHIEF EXECUTIVE OFFICER
           PURSUANT TO 18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

      In connection with the quarterly report on Form 10-Q of Cox
Communications, Inc. (the "Company") for the period ended March 31, 2005, as
filed with the Securities and Exchange Commission as of the date hereof, I,
James O. Robbins, 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 the best of
my knowledge:

      (1) the Report fully complies with the requirements of Section 13(a) or
15(d)of the Securities Exchange Act of 1934, as amended; and

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

                                   /s/ James O. Robbins
                                   Name: James O. Robbins
                                   Title: President and Chief Executive Officer
                                   Date: May 9, 2005

A signed original of this written statement required by Section 906 or other
documentation authenticating, acknowledging, or otherwise adopting the signature
that appears in typed form within the electronic version of this written
statement required by Section 906, has been provided to Cox Communications, Inc.
and will be retained by Cox Communications, Inc. and furnished to the Securities
and Exchange Commission or its staff upon request.

This certification "accompanies" the quarterly report on Form 10-Q to which it
relates, is not deemed filed with the Securities and Exchange Commission, and is
not to be incorporated by reference into any filing of Cox Communications, Inc.
under the Securities Act of 1933, as amended, or the Securities Exchange Act of
1934, as amended (whether made before or after the date of the quarterly report
on Form 10-Q, irrespective of any general incorporation language contained in
such filing).