UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

FORM 10-D

ASSET-BACKED ISSUER
DISTRIBUTION REPORT PURSUANT TO SECTION 13 OR 15(d) OF
THE SECURITIES EXCHANGE ACT OF 1934

For the monthly distribution period from
May 13, 2023 to June 12, 2023

Commission File Number of Issuing entity:

333-179413-01

Central Index Key Number of issuing entity:

0001571238

UBS-Barclays Commercial Mortgage Trust 2013-C6
(Exact name of issuing entity as specified in its charter)

Commission File Number of depositor:

333-179413

Central Index Key Number of depositor:

0001541480

Barclays Commercial Mortgage Securities LLC
(Exact name of depositor as specified in its charter)

Central Index Key Number of sponsor: 0001541886
UBS Real Estate Securities Inc.
(Exact name of sponsor as specified in its charter)

Central Index Key Number of sponsor: 0000312070
Barclays Bank PLC
(Exact name of sponsor as specified in its charter)

Central Index Key Number of sponsor: 0001542256
Natixis Real Estate Capital LLC
(Exact name of sponsor as specified in its charter)

Central Index Key Number of sponsor: 0001567746
Redwood Commercial Mortgage Corporation
(Exact name of sponsor as specified in its charter)

Daniel J. Vinson (212) 528-8224
(Name and telephone number, including area code, of the person to contact in connection with this filing)

New York
(State or other jurisdiction of incorporation or organization of the issuing entity)

27-010880
(I.R.S. Employer Identification No.)

				c/o U.S. Bank Trust Company, National Association
190 South Lasalle Street
Chicago, IL
(Address of principal executive offices of issuing entity)

60603
(Zip Code)

(312)-332-7535
(Telephone number, including area code)

None
(Former name, former address, if changed since last report)

Registered/reporting pursuant to (check one)

				Name of exchange
Title of Class	Section 12(b)	Section 12(g)	Section 15(d)	(If Section 12(b))

Class A-1	☐	☐	☒	Not Applicable
Class A-2	☐	☐	☒	Not Applicable
Class A-3	☐	☐	☒	Not Applicable
Class A-4	☐	☐	☒	Not Applicable
Class A-SB	☐	☐	☒	Not Applicable
Class A-S	☐	☐	☒	Not Applicable

Indicate by check mark whether the registrant (1) filed all reports required to be filed by Section 13 or 15(d) of the Securities and Exchange Act of 1934 during the preceding 12 months (or for such shorter period that the registrant was required to file such reports), and (2) has been subject to such filing requirements for the past 90 days? Yes ☒ No ☐

PART I - DISTRIBUTION INFORMATION

Item 1. Distribution and Pool Performance Information.
On June 12, 2023 a distribution was made to holders of the certificates issued by UBS-Barclays Commercial Mortgage Trust 2013-C6. The distribution report is attached as an Exhibit to this Form 10-D, please see Item 9(b) Exhibit 99.1 for the related information.

No assets securitized by Barclays Commercial Mortgage Securities LLC (the 'Depositor') and held by UBS-Barclays Commercial Mortgage Trust 2013-C6 were the subject of a demand to repurchase for breach of the representations and warranties contained in the underlying transaction documents during the distribution period from May 13, 2023 to June 12, 2023.

The Depositor has filed a Form ABS-15G pursuant to Rule 15Ga-1 under The Exchange Act of 1934 on May 05, 2023. The CIK number of the Depositor is 0001541480.

UBS Real Estate Securities Inc., one of the sponsors, has filed a Form ABS-15G pursuant to Rule 15Ga-1 under The Exchange Act of 1934 on May 09, 2023. The CIK number of UBS Real Estate Securities Inc. is 0001541886.

Barclays Bank PLC, one of the sponsors, has filed a Form ABS-15G pursuant to Rule 15Ga-1 under The Exchange Act of 1934 on May 05, 2023. The CIK number of Barclays Bank PLC is 0000312070.

Natixis Real Estate Capital LLC, one of the sponsors, has filed a Form ABS-15G pursuant to Rule 15Ga-1 under The Exchange Act of 1934 on February 14, 2023. The CIK number of Natixis Real Estate Capital LLC is 0001542256.

Redwood Commercial Mortgage Corporation, one of the sponsors, has filed a Form ABS-15G pursuant to Rule 15Ga-1 under The Exchange Act of 1934 on February 10, 2023. The CIK number of Redwood Commercial Mortgage Corporation is 0001567746.

Item 1A. Asset-Level Information.
Not applicable.

Item 1B. Asset Representations Reviewer and Investor Communication.
Not applicable.

PART II - OTHER INFORMATION

Item 2. Legal Proceedings.
None

Item 3. Sales of Securities and Use of Proceeds.
None

Item 4. Defaults Upon Senior Securities.
None

Item 5. Submission of Matters to a Vote of Security Holders.
None

Item 6. Significant Obligors of Pool Assets.
The Gateway mortgaged property constitutes a significant obligor within the meaning of item 1101 (k)(2) of Regulation AB and as disclosed in the Prospectus Supplement for UBS-Barclays Commercial Mortgage Trust 2013-C6.
Based on the borrower's operating statement with an end date of March 31, 2023, the Gateway mortgage loan has a 2023 Net Operating Income of $3,524,234.09 as of March 31, 2023.

Item 7. Change in Sponsor Interest in the Securities.
None

Item 8. Significant Enhancement Provider Information.
Not Applicable

Item 9. Other Information.
None

Item 10. Exhibits.
(a) The following is a list of documents filed as part of this Report on Form 10-D:
(99.1) Monthly report distributed to holders of UBS-Barclays Commercial Mortgage Trust 2013-C6, relating to the June 12, 2023 distribution.


(b) The exhibits required to be filed by the Registrant pursuant to this form are listed in the Exhibit Index that immediately follows on the signature page hereof.

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned thereunto duly authorized.

									Barclays Commercial Mortgage Securities LLC
									(Depositor)

Date: June 21, 2023									/s/ Daniel Vinson
									Name: Daniel Vinson
									Title: CEO

Exhibit Number	Description
Exhibit 99.1	Monthly report distributed to holders of the certificates issued by UBS-Barclays Commercial Mortgage Trust 2013-C6, relating to the June 12, 2023 distribution.

UBS-Barclays Commercial Mortgage Trust 2013-C6 10-D