Exhibit (a)(1)(C)

Offer To Purchase For Cash

All Outstanding Shares of Common Stock

of

CoreSite Realty Corporation

a Maryland corporation

at

$170.00 Per Share in Cash

Pursuant to the Offer to Purchase

Dated November 29, 2021

by

Appleseed Merger Sub LLC

a wholly owned direct subsidiary of

Appleseed Holdco LLC

and a wholly owned indirect subsidiary of

American Tower Investments LLC

a wholly owned indirect subsidiary of

American Tower Corporation

THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT ONE MINUTE AFTER

11:59 P.M., EASTERN TIME, ON DECEMBER 27, 2021,

UNLESS THE OFFER IS EXTENDED OR EARLIER TERMINATED.

November 29, 2021

To Brokers, Dealers, Commercial Banks, Trust Companies and Other Nominees:

We have been engaged by Appleseed Merger Sub LLC, a Maryland limited liability company (“Purchaser”) and a wholly owned direct subsidiary of Appleseed Holdco LLC, a Delaware limited liability company (“Holdco”), and a wholly owned indirect subsidiary of American Tower Investments LLC, a California limited liability company (“Parent”), and a wholly owned indirect subsidiary of American Tower Corporation, a Delaware corporation (“ATC”), to act as Information Agent in connection with Purchaser’s offer to purchase all of the outstanding shares of common stock, par value $0.01 per share (the “Shares”), of CoreSite Realty Corporation, a Maryland corporation (“CoreSite”), at a price of $170.00 per Share (the “Offer Price”) without interest and subject to any applicable withholding taxes, net to the seller in cash , upon the terms and subject to the conditions set forth in the Offer to Purchase dated November 29, 2021 (the “Offer to Purchase”), and the related Letter of Transmittal (the “Letter of Transmittal” and which, together with the Offer to Purchase, each as may be amended or supplemented from time to time, constitute the “Offer”) enclosed herewith. Please furnish copies of the enclosed materials to those of your clients for whom you hold Shares registered in your name or in the name of your nominee.

THE BOARD OF DIRECTORS OF CORESITE HAS UNANIMOUSLY RECOMMENDED THAT STOCKHOLDERS ACCEPT THE OFFER AND TENDER ALL OF THEIR SHARES TO PURCHASER PURSUANT TO THE OFFER.

The Offer is not subject to any financing condition. The conditions to the Offer are described in Section 13 of the Offer to Purchase.

For your information and for forwarding to your clients for whom you hold Shares registered in your name or in the name of your nominee, we are enclosing the following documents:

1. The Offer to Purchase;

2. The Letter of Transmittal for your use in accepting the Offer and tendering Shares and for the information of your clients, together with the included Internal Revenue Service Form W-9;

3. A form of letter which may be sent to your clients for whose accounts you hold Shares registered in your name or in the name of your nominee, with space provided for obtaining such clients’ instructions with regard to the Offer; and

4. CoreSite’s Solicitation/Recommendation Statement on Schedule 14D-9, dated November 29, 2021.

We urge you to contact your clients as promptly as possible. Please note that the Offer and withdrawal rights will expire at one minute after 11:59 p.m., Eastern Time, on December 27, 2021, unless the Offer is extended or earlier terminated.

The Offer is being made in connection with the Agreement and Plan of Merger, dated as of November 14, 2021 (together with any amendments or supplements thereto, the “Merger Agreement”), among Parent, Holdco, Purchaser, Appleseed OP Merger Sub LLC, a Delaware limited liability company and wholly owned direct subsidiary of Holdco (“OP Merger Sub”), CoreSite, CoreSite, L.P., a Delaware limited partnership and subsidiary of CoreSite (the “OP”), and ATC, pursuant to which, after the completion of the Offer and the satisfaction or waiver of certain conditions, Purchaser will be merged with and into CoreSite, without a vote of CoreSite’s stockholders in accordance with Section 3-106.1 of the Maryland General Corporation Law (the “MGCL”), and CoreSite will be the surviving corporation and a direct wholly-owned subsidiary of Holdco (the “Interim Surviving Entity”, and such merger, the “REIT Merger”). Substantially concurrently with the REIT Merger, OP Merger Sub will merge with and into the OP, with the OP continuing as the surviving limited partnership (the “OP Merger”). Immediately following the REIT Merger and the OP Merger, the Interim Surviving Entity will merge with and into Holdco, with Holdco continuing as the surviving limited liability company (such limited liability company, the “Surviving Entity”, and such merger, the “Holdco Merger”, and together with the REIT Merger and the OP Merger, the “Mergers”) At the effective time of the REIT Merger, each Share outstanding immediately prior to the effective time of the REIT Merger (other than (i) certain restricted shares and (ii) Shares held by Parent, Holdco, Purchaser or OP Merger Sub) will be converted into the right to receive consideration equal to the Offer Price, upon the terms and subject to the conditions set forth in the Merger Agreement. At the effective time of the OP Merger, each partnership unit issued and outstanding and held by a limited partner of the OP (excluding CoreSite) will be converted into the right to receive an amount in cash equal to the Offer Price. As a result of the REIT Merger, CoreSite would cease to be a publicly traded company and will become wholly owned by Holdco.

THE BOARD OF DIRECTORS OF CORESITE HAS UNANIMOUSLY RECOMMENDED THAT STOCKHOLDERS ACCEPT THE OFFER AND TENDER ALL OF THEIR SHARES TO PURCHASER PURSUANT TO THE OFFER.

For Shares to be properly tendered pursuant to the Offer, the share certificates or confirmation of receipt of such Shares under the procedure for book-entry transfer, together with a properly completed and duly executed Letter of Transmittal, including any required signature guarantees, or, in the case of book-entry transfer, either such Letter of Transmittal or an Agent’s Message (as defined in Section 3 of the Offer to Purchase) in lieu of such Letter of Transmittal, and any other documents required in the Letter of Transmittal, must be timely received by the Depositary in accordance with the Offer to Purchase and the Letter of Transmittal.

Except as set forth in the Offer to Purchase, Purchaser will not pay any fees or commissions to any broker or dealer or other person, other than to us, as the information agent, and American Stock Transfer & Trust Company, LLC, as the depositary, for soliciting tenders of Shares pursuant to the Offer. Purchaser will, however, upon request, reimburse brokers, dealers, commercial banks, trust companies and other nominees for customary mailing and handling expenses incurred by them in forwarding the offering material to their customers. Purchaser will pay all stock transfer taxes applicable to its purchase of Shares pursuant to the Offer, subject to Instruction 6 of the Letter of Transmittal.

Any inquiries you may have with respect to the Offer should be addressed to, and additional copies of the enclosed materials may be obtained from, the undersigned at the address and telephone numbers set forth below.

Very truly yours,

Innisfree M&A Incorporated

Nothing contained herein or in the enclosed documents shall render you the agent of ATC, Parent, Holdco, Purchaser, the Information Agent or the Depositary or any affiliate of any of them or authorize you or any other person to use any document or make any statement on behalf of any of them in connection with the Offer other than the enclosed documents and the statements contained therein.

The Information Agent for the Offer is:

Innisfree M&A Incorporated

501 Madison Avenue, 20th Floor

New York, NY 10022

Banks and Brokerage Firms Call: (212) 750-5833

Stockholders Call Toll Free: (877) 717-3904