EXHIBIT 32.1

Certification

     Pursuant to 18 U.S.C. § 1350, the undersigned officer of The Goldman Sachs Group, Inc. (the “Company”) hereby certifies that the Company’s Quarterly Report on Form 10-Q for the quarter ended August 27, 2004 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d), as applicable, of the Securities Exchange Act of 1934 and that the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: October 8, 2004	/s/ HENRY M. PAULSON, JR.
	Henry M. Paulson, Jr.
	Chief Executive Officer

     The foregoing certification is being furnished solely pursuant to 18 U.S.C. § 1350 and is not being filed as part of the Report or as a separate disclosure document.

Certification

     Pursuant to 18 U.S.C. § 1350, the undersigned officer of The Goldman Sachs Group, Inc. (the “Company”) hereby certifies that the Company’s Quarterly Report on Form 10-Q for the quarter ended August 27, 2004 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d), as applicable, of the Securities Exchange Act of 1934 and that the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: October 8, 2004	/s/ DAVID A. VINIAR
	David A. Viniar
	Chief Financial Officer

     The foregoing certification is being furnished solely pursuant to 18 U.S.C. § 1350 and is not being filed as part of the Report or as a separate disclosure document.