Exhibit 32.1

CERTIFICATION PURSUANT TO

SECTION 1350, CHAPTER 63 OF TITLE 18, UNITED STATES CODE,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

Pursuant to Section 1350, Chapter 63 of Title 18, United States Code, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned, as Chief Executive Officer of Blue Owl Capital Corporation III (the “Company”), does hereby certify that to the undersigned’s knowledge:

1)the Company’s Form 10-Q for the quarter ended March 31, 2024 fully complies with the requirements of Section 13(a) or 15(d), as applicable, of the Securities Exchange Act of 1934, as amended; and

2)the information contained in the Company’s Form 10-Q for the quarter ended March 31, 2024 fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: May 8, 2024	By:	/s/ Craig W. Packer
		Craig W. Packer
		Chief Executive Officer