Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We hereby consent to the use in the Prospectus constituting a part of this Registration Statement on Form S-1 of our report dated September 29, 2025, relating to the financial statements of Black Spade Acquisition III Co as of and for the period from August 21, 2025 (inception) through September 5, 2025, which is contained in that Prospectus. We also consent to the reference to us under the caption “Experts” in the Prospectus.

/s/ WithumSmith+Brown, PC

New York, New York

September 29, 2025