Exhibit 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350, 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 HPS Corporate Capital Solutions Fund (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) of the Securities Exchange Act of 1934; 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 15, 2024

By:			/s/ Michael Patterson
			Michael Patterson
			Chief Executive Officer