BlackRock Core Bond Trust

Cusip: 09249E101

Ticker: BHK

Record Date	June 15, 2020
Pay Date	June 30, 2020
Distribution Amount per share	$                0.067600

The following table sets forth the estimated amounts of the current distribution and the cumulative distributions paid this fiscal year to date from the following sources: net investment income, net realized capital gains and return of capital. All amounts are expressed per common share.

							% Breakdown of the
			% Breakdown		Total Cumulative		Total Cumulative
			of the Current		Distributions for the		Distributions for the
	Current Distribution		Distribution		Fiscal Year to Date		Fiscal Year to Date
Net Investment Income	$	0.066395		98%	$	0.336795		100%
Net Realized Capital Gains	$	-		0%	$	-		0%
Return of Capital	$	0.001205		2%	$	0.001205		0%
Total (per common share)	$	0.067600		100%	$	0.338000		100%
Average annual total return (in relation to NAV) for the 5-year period ending on May 31, 2020								7.15%
Annualized current distribution rate expressed as a percentage of NAV as of May 31, 2020								5.20%
Cumulative total return (in relation to NAV) for the fiscal year through May 31, 2020								3.71%
Cumulative fiscal year distributions as a percentage of NAV as of May 31, 2020								1.73%

You should not draw any conclusions about the Fund’s investment performance from the amount of this distribution or from the terms of the Funds Managed Distribution Plan.

The Fund estimates that it has distributed more than its net investment income and net realized capital gains; therefore, a portion of your distribution may be a return of capital. A return of capital may occur, for example, when some or all of the money that you invested in the Fund is paid back to you. A return of capital does not necessarily reflect the Fund’s investment performance and should not be confused with ‘yield’ or ‘income’. When distributions exceed total return performance, the difference will reduce the Fund’s net asset value per share.

The amounts and sources of distributions reported in this Notice are only estimates and are not being provided for tax reporting purposes. The actual amounts and sources of the amounts for tax reporting purposes will depend upon the Fund’s investment experience during its fiscal year and may be subject to changes based on tax regulations. The Fund will send you a Form 1099-DIV for the calendar year that will tell you how to report these distributions for federal income tax purposes.

Contact Number:  800-882-0052

BlackRock Core Bond Trust

Cusip: 09249E101

Ticker: BHK

Record Date	July 15, 2020
Pay Date	July 31, 2020
Distribution Amount per share	$                    0.067600

The following table sets forth the estimated amounts of the current distribution and the cumulative distributions paid this fiscal year to date from the following sources: net investment income, net realized capital gains and return of capital. All amounts are expressed per common share.

							% Breakdown of the
			% Breakdown		Total Cumulative		Total Cumulative
			of the Current		Distributions for the		Distributions for the
	Current Distribution		Distribution		Fiscal Year to Date		Fiscal Year to Date
Net Investment Income	$	0.061235		91%	$	0.397894		98%
Net Realized Short-Term Capital Gains	$	0.006365		9%	$	0.007706		2%
Net Realized Long-Term Capital Gains	$	-		0	$	-		0%
Return of Capital	$	-		0%	$	-		0%
Total (per common share)	$	0.067600		100%	$	0.405600		100%
Average annual total return (in relation to NAV) for the 5-year period ending on June 30, 2020								8.24%
Annualized current distribution rate expressed as a percentage of NAV as of June 30, 2020								5.11%
Cumulative total return (in relation to NAV) for the fiscal year through June 30, 2020								6.10%
Cumulative fiscal year distributions as a percentage of NAV as of June 30, 2020								2.13%

You should not draw any conclusions about the Fund’s investment performance from the amount of this distribution or from the terms of the Funds Managed Distribution Plan.

The amounts and sources of distributions reported in this Notice are only estimates and are not being provided for tax reporting purposes. The actual amounts and sources of the amounts for tax reporting purposes will depend upon the Fund’s investment experience during its fiscal year and may be subject to changes based on tax regulations. The Fund will send you a Form 1099-DIV for the calendar year that will tell you how to report these distributions for federal income tax purposes.

Contact Number: 800-882-0052