SECTION 906 CERTIFICATION

Pursuant to 18 U.S.C. § 1350, the undersigned officers of BlackRock Core Bond Trust (the "Company"), hereby certifies, to the best of their knowledge, that the Company's Report on Form N-CSR for the period ended April 30, 2005, (the "Report") fully complies with the requirements of Section 13(a) or 15(d), as applicable, of the Securities Exchange Act of 1934 and that the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: July 1, 2005

/s/ Robert S. Kapito
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Name: Robert S. Kapito
Title: Principal Executive Officer

/s/ Henry Gabbay
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Name: Henry Gabbay
Title: Principal Financial Officer