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 Annual Report on Form 10-K of the Company for the year ended December 31, 2011 (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.

Dated: February 24, 2012

/s/ Thomas M. Ray

Thomas M. Ray

Chief Executive Officer