Exhibit 32.1

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Certification of Chief Executive Officer Pursuant to 18 U.S.C. Section 1350,

as Adopted Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

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Pursuant to 18 U.S.C. § 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned officer of CoreSite Realty Corporation (the “Company”) hereby certifies, to such officer’s knowledge, that:

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(i) The accompanying Quarterly Report on Form 10-Q of the Company for the quarter ended June 30, 2020 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

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(ii) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company for the period covered by the Report.

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Dated: July 31, 2020

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