Exhibit 23.1

INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM’S CONSENT

We consent to the incorporation by reference in the Registration Statement (Form S-8 No.333-29987) pertaining to the Savings Banks Employees Retirement Association 401(k) Plan as adopted by Century Bancorp, Inc., of our report dated July 15, 2013, with respect to the financial statements and schedule of the Savings Banks Employees Retirement Association 401(k) Plan as adopted by Century Bancorp, Inc., included in this Annual Report on Form 11-K for the year ended December 31, 2012.

/s/ Marcum LLP

Boston, MA

July 15, 2013