CoreSite Realty 10-Q 2018 Q2 Quarterly report

Exhibit 32.1

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

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:

(i) The accompanying Quarterly Report on Form 10-Q of the Company for the quarter ended June 30, 2018 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

(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.

Dated: July 27, 2018

/s/ Paul E. Szurek

Paul E. Szurek

Chief Executive Officer