Exhibit 7.04

[Letterhead]

August 1, 2004

Members of the Board:

     Cox Enterprises, Inc. (CEI) is pleased to offer to acquire the outstanding shares of Class A common stock of Cox Communications, Inc. (CCI) not currently owned by CEI at a purchase price of $32 per share. Through this offer it is our intention that CCI becomes a wholly owned subsidiary of CEI.

     We believe that our offer is fair to and in the best interest of CCI and its public shareholders. Although this transaction does not represent a change of control, this offer price represents a 16% premium over Friday’s closing price and a 14% premium to the average trading price of the Class A common stock for the last ten days.

     We believe our proposal makes great sense for CEI and its future. The competitive demands of the cable industry when balanced against the need for a public company to be vigilant with respect to short-term results have convinced us that private ownership of this business is desirable and will assist CCI in attaining its business objectives.

     We expect that the Board of Directors of CCI will form a special committee of independent directors to respond to our proposal on behalf of CCI’s public shareholders. Our representatives on the CCI board will vote in favor of that delegation of authority. We also encourage the special committee to retain its own legal and financial advisors to assist in its review. CEI would welcome the opportunity to present its proposal to the special committee as soon as possible. Our entire team, including our legal and financial advisors, looks forward to working with the special committee and its legal and financial advisors to complete a mutually acceptable transaction.

     Following the successful conclusion of our discussions with the special committee and execution of a merger agreement, we would propose to initiate the transaction through a tender offer. The tender offer would be conditioned on the tender of a number of Class A common shares sufficient to bring CEI’s ownership interest in the Class A common shares to 90%. We have received firm financing commitments from Citigroup and Lehman Brothers that would enable us to complete the transaction, refinance existing indebtedness and provide liquidity for additional working capital. We anticipate acquiring any shares not purchased in the tender through a merger, at the same cash price per share as the tender offer.

     In considering our proposal, you should be aware that we are interested only in acquiring the publicly held CCI shares and we will not sell our stake in CCI.

     Concurrently with sending this offer to you, we are filing a 13-D amendment, and as such, we feel compelled to issue a press release. A copy of the press release announcing our intention to commence this process is attached for your information. We expect to issue the press release the morning of August 2nd prior to opening of trading.

     Thank you for your consideration.

     /s/ James C. Kennedy