Cobalt International Energy 10-Q 2015 Q1 Quarterly report

QuickLinks -- Click here to rapidly navigate through this document

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 Cobalt International Energy, Inc. (the "Company") for the quarterly period ended March 31, 2015 as filed with the Securities and Exchange Commission on the date hereof (the "Report"), Joseph H. Bryant, as Chief Executive Officer of the Company, hereby certifies, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to his 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 results of operations of the Company.

By:	/s/ JOSEPH H. BRYANT
	Name:	Joseph H. Bryant
	Title:	Chairman of the Board of Directors and Chief Executive Officer

Date: May 5, 2015

A signed original of this written statement required by Section 906, or other document 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 the Company and will be retained by the Company and furnished to the Securities and Exchange Commission or its staff upon request.

QuickLinks

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