CERC Cerecor Inc

Filed Pursuant to Rule 424(b)(3)

Registration No. 333-204905

Prospectus Supplement No. 21

(To Prospectus dated October 14, 2015)

4,000,000 shares of common stock issuable upon the

exercise of the 4,000,000 outstanding Class A warrants

and

2,000,000 shares of common stock issuable upon the

exercise of the 4,000,000 outstanding Class B warrants

This prospectus supplement No. 21 supplements the prospectus dated October 14, 2015 filed pursuant to Rule 424(b)(4) by Cerecor Inc. (the “Company” or “we”), as supplemented by the prospectus supplement No. 1 dated October 20, 2015, the prospectus supplement No. 2 dated November 13, 2015, the prospectus supplement No. 3 dated November 23, 2015, the prospectus supplement No. 4 dated December 17, 2015, the prospectus supplement No. 5 dated December 21, 2015, the prospectus supplement No. 6 dated December 29, 2015, the prospectus supplement No. 7 dated January 5, 2016, the prospectus supplement No. 8 dated January 12, 2016, the prospectus supplement No. 9 dated January 19, 2016, the prospectus supplement No. 10 dated February 2, 2016, the prospectus supplement No. 11 dated April 11, 2016, the prospectus supplement No. 12 dated May 25, 2016, the prospectus supplement No. 13 dated May 26, 2016, the prospectus supplement No. 14 dated May 26, 2016, the prospectus supplement No. 15 dated July 20, 2016, the prospectus supplement No. 16 dated August 15, 2016, the prospectus supplement No. 17 dated August 29, 2016, the prospectus supplement No. 18 dated September 6, 2016, the prospectus supplement No. 19 dated September 12, 2016 and the prospectus supplement No. 20 dated September 21, 2016, each filed pursuant to Rule 424(b)(3) by the Company (collectively, the “Prospectus”).  Pursuant to the Prospectus, this prospectus supplement relates to the continuous offering of 4,000,000 shares of common stock underlying our Class A warrants and 2,000,000 shares of our common stock underlying Class B warrants.  Each warrant was a component of a unit that we issued in our initial public offering, which closed on October 20, 2015.  The components of the units began to trade separately on November 13, 2015.  Each Class A warrant became exercisable on the date when the units detached and the components began to trade separately and will expire on October 20, 2018, or earlier upon redemption.  Each Class B warrant became exercisable on the date the units detached and the components began to trade separately and will expire on April 20, 2017.

This prospectus supplement incorporates into our Prospectus the information contained in our attached Current Report on Form 8-K, which was filed with the Securities and Exchange Commission on September 26, 2016.

You should read this prospectus supplement in conjunction with the Prospectus, including any supplements and amendments thereto. This prospectus supplement is qualified by reference to the Prospectus except to the extent that the information in this prospectus supplement supersedes the information contained in the Prospectus.

This prospectus supplement is not complete without, and may not be delivered or utilized except in connection with, the Prospectus, including any supplements and amendments thereto.

Our common stock, the Class A warrants and the Class B warrants are traded on The NASDAQ Capital Market under the symbols “CERC,” “CERCW,” and “CERCZ,” respectively.

AN INVESTMENT IN OUR SECURITIES INVOLVES A HIGH DEGREE OF RISK. SEE THE

SECTION ENTITLED “RISK FACTORS” BEGINNING ON PAGE 16 OF THE PROSPECTUS

FOR A DISCUSSION OF INFORMATION THAT SHOULD BE CAREFULLY CONSIDERED IN CONNECTION WITH AN INVESTMENT IN OUR SECURITIES

Neither the Securities and Exchange Commission nor any state securities commission has

approved or disapproved of these securities or determined if this Prospectus is truthful

or complete. Any representation to the contrary is a criminal offense.

The date of this prospectus supplement is September 26, 2016

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

FORM 8-K

CURRENT REPORT

Pursuant to Section 13 or 15(d) of

the Securities Exchange Act of 1934

Date of Report (Date of earliest event reported): September 22, 2016

Registrant’s Telephone Number, Including Area Code: (410) 522-8707

Not Applicable

(Former Name or Former Address, if Changed Since Last Report)

Check the appropriate box below if the Form 8-K filing is intended to simultaneously satisfy the filing obligation of the registrant under any of the following provisions (see General Instructions A.2. below):

☐ Written communications pursuant to Rule 425 under the Securities Act (17 CFR 230.425)

☐ Soliciting material pursuant to Rule 14a-12 under the Exchange Act (17 CFR 240.14a-12)

☐ Pre-commencement communications pursuant to Rule 14d-2(b) under the Exchange Act (17 CFR 240.14d-2(b))

☐ Pre-commencement communications pursuant to Rule 13e-4(c) under the Exchange Act (17 CFR 240.13e-4(c))

Item 1.01. Entry into a Material Definitive Agreement.

Exclusive License, Development and Commercialization Agreement

On September 22, 2016, the Company entered into an exclusive license, development and commercialization agreement (the “Exclusive License Agreement”) with Eli Lilly and Company (“Lilly”) pursuant to which the Company received exclusive, global rights to develop and commercialize LY3130481, now designated as CERC-611, a potent and selective Transmembrane AMPA Receptor Regulatory Proteins (“TARP”)-γ8-dependent AMPA receptor antagonist. 

The Company’s rights under the Exclusive License Agreement are exclusive (even as to Lilly) for the term of the Exclusive License Agreement, with the right to grant sublicenses through multiple tiers. Lilly retains rights for internal, non-clinical research purposes. The Company is obligated under the Exclusive License Agreement to use commercially reasonable efforts to develop and commercialize CERC-611 at its expense. If Lilly obtains a license for any future patent rights or know-how necessary for the development, commercialization or manufacture under the Exclusive License Agreement, the Company has the right, but not the obligation, to consent to include such patent rights or know-how, as well as the right to terminate any such license in the Company’s discretion.

The terms of the Exclusive License Agreement provide for an upfront payment of $2.0 million, of which $750,000 is due within 30 days of the effective date of the Exclusive License Agreement, and the remaining balance of $1.25 million is due after the first subject is dosed with CERC-611 in a multiple ascending dose study. The terms of the Exclusive License Agreement also require that the Company make one-time development, commercialization and sales milestone payments to Lilly of up to $67.5 million. When and if commercial sales of CERC-611 begin, the Company will be obligated to pay Lilly a royalty in the mid-single digits to low double digits based on net sales.

The Exclusive License Agreement also includes customary representations, warranties and covenants. Subject to certain exceptions and limitations, each of the Company and Lilly has agreed to indemnify the other for breaches of representations, warranties and covenants and other specified matters. Unless terminated earlier, the Exclusive License Agreement will remain in effect, on a country-by-country basis and product-by-product basis, until the parties’ royalty obligations end. Both parties have a right to terminate the Exclusive License Agreement if the other party enters bankruptcy, upon an uncured breach by the other party or if the other party challenges its patents relating to the licensed technology. The Exclusive License Agreement will be filed as an exhibit to our Quarterly Report on Form 10-Q for the quarter ended September 30, 2016.

Item 8.01. Other Events.

The Company issued the press release attached hereto as Exhibit 99.1 regarding the license.