EXHIBIT 32.1

CERTIFICATION OF PRINCIPAL EXECUTIVE OFFICER AND PRINCIPAL FINANCIAL OFFICER PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002 (18 U.S.C. 1350)

In connection with the Annual Report of Wells Core Office Income REIT, Inc. (the “Registrant”) on Form 10-K for the year ended December 31, 2010, as filed with the Securities and Exchange Commission (the “Report”), the undersigned, Leo F. Wells, III, Principal Executive Officer of the Registrant, and Douglas P. Williams, Principal Financial Officer of the Registrant, hereby certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (18 U.S.C. 1350) that, to the best of our knowledge and belief:

(1) The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Registrant.

It is not intended that this statement be deemed to be filed for purposes of the Securities Exchange Act of 1934.

/s/ Leo F. Wells, III

Leo F. Wells, III

Principal Executive Officer

March 28, 2011

/s/ Douglas P. Williams

Douglas P. Williams

Principal Financial Officer

March 28, 2011