COLUMBUS CIRCLE CAPITAL CORP III

Exhibit 10.6

COLUMBUS CIRCLE CAPITAL CORP III

▇ ▇▇▇▇▇▇▇▇ ▇▇▇▇▇▇, ▇▇▇▇ ▇▇▇▇▇

New York NY, 10019

July 8, 2026

▇▇▇▇▇ & Company LLC

▇ ▇▇▇▇▇▇▇▇ ▇▇▇▇▇▇, ▇▇▇▇ ▇▇▇▇▇

New York NY, 10019

Re: Administrative Services Agreement

Ladies and Gentlemen:

This letter agreement by and between Columbus Circle Capital Corp III (the “Company”) and ▇▇▇▇▇ & Company LLC (the “Services Provider”), dated as of the date hereof, will confirm our agreement that, commencing on the date the securities of the Company are first listed on the Nasdaq Global Market (the “Listing Date”), pursuant to a Registration Statement on Form S-1 and prospectus filed with the U.S. Securities and Exchange Commission (the “Registration Statement”) and continuing until the earlier of the consummation by the Company of an initial business combination and the Company’s liquidation (in each case as described in the Registration Statement) (such earlier date hereinafter referred to as the “Termination Date”):

(i) The Services Provider shall make available (or cause other persons to make available) to the Company, at ▇ ▇▇▇▇▇▇▇▇ ▇▇▇▇▇▇, ▇▇▇▇ ▇▇▇▇▇, ▇▇▇ ▇▇▇▇ ▇▇ ▇▇▇▇▇ (or any successor location of the Services Provider), certain office space, utilities and secretarial and administrative support as may be reasonably required by the Company. As reimbursement therefor, the Company shall pay the Services Provider (and the Services Provider will receive on behalf of itself or, to the extent it causes another person to make support available to the Company, as nominee on behalf of such other person) the sum of $10,000 per month beginning on the Listing Date and continuing monthly thereafter until the Termination Date.

(ii) The Services Provider hereby irrevocably waives any and all right, title, interest, causes of action and claims of any kind as a result of, or arising out of, this letter agreement (each, a “Claim”) in or to, and any and all right to seek payment of any amounts due to it out of, the trust account established for the benefit of the public shareholders of the Company and into which substantially all of the proceeds of the Company’s initial public offering will be deposited (the “Trust Account”), and hereby irrevocably waives any Claim it may have in the future, which Claim would reduce, encumber or otherwise adversely affect the Trust Account or any monies or other assets in the Trust Account, and further agrees not to seek recourse, reimbursement, payment or satisfaction of any Claim against the Trust Account or any monies or other assets in the Trust Account for any reason whatsoever.

This letter agreement constitutes the entire agreement and understanding of the parties hereto in respect of its subject matter and supersedes all prior understandings, agreements or representations by or among the parties hereto, written or oral, to the extent they relate in any way to the subject matter hereof or the transactions contemplated hereby.

This letter agreement may not be amended, modified or waived as to any particular provision, except by a written instrument executed by the parties hereto.

No party hereto may assign either this letter agreement or any of its rights, interests or obligations hereunder without the prior written approval of the other party; provided, however, that the Services Provider may assign this letter agreement, in whole or in part, to Services Provider or any other person that directly, or indirectly through one or more intermediaries, controls, or is controlled by, or is under common control with, Services Provider without the prior written approval of the Company. Any purported assignment in violation of this paragraph shall be void and ineffectual and shall not operate to transfer or assign any interest or title to the purported assignee.

This letter agreement constitutes the entire relationship of the parties hereto, and any litigation between the parties (whether grounded in contract, tort, statute, law or equity) shall be governed by, construed in accordance with and interpreted pursuant to the laws of the State of New York, without giving effect to its choice of laws principles.

[Signature Page Follows]

Very truly yours,
COLUMBUS CIRCLE CAPITAL CORP III
By:	/s/ ▇▇▇▇ ▇▇▇▇
Name:	▇▇▇▇ ▇▇▇▇
Title:	Chief Executive Officer

AGREED TO AND ACCEPTED BY:
▇▇▇▇▇ & COMPANY LLC
By:	/s/ ▇▇▇▇▇▇ ▇▇▇▇▇▇
Name:	▇▇▇▇▇▇ ▇▇▇▇▇▇
Title:	Authorized Signature

[SIGNATURE PAGE TO ADMINISTRATIVE SERVICES AGREEMENT]