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

In connection with the Quarterly Report of Apex Treasury Corporation (the “Company”) on Form 10-Q for the quarterly period ended September 30, 2025, as filed with the Securities and Exchange Commission (the “Report”), we, Ajmal Rahman and Hugh Cochrane, Co-Principal Executive Officers of the Company, certify, pursuant to 18 U.S.C. §1350, as adopted pursuant to §906 of the Sarbanes-Oxley Act of 2002, that, to the best of our 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.

Dated: December 5, 2025

/s/ Ajmal Rahman

Ajmal Rahman

Co-Chief Executive Officer and Chairman

(Co-Principal Executive Officer)

/s/ Hugh Cochrane

Hugh Cochrane

Co-Chief Executive Officer

(Co-Principal Executive Officer)