Having shared my view in above post, I also feel that there is a workable argument which you can build in this case:
Proviso to section 50
Provided that the interest on tax payable in respect of supplies made during a tax period and declared in the return for the said period furnished after the due date in accordance with the provisions of section 39, except where such return is furnished after commencement of any proceedings under section 73 or section 74 in respect of the said period, shall be payable on that portion of the tax which is paid by debiting the electronic cash ledger.
Factual points to be considered:-
1. The supplies made in Aug 2019 for Rs.37,62,215.98 as cess has been duly declared in GSTR-1 of August 2019.
2. The supplies made in Aug 2019 has also been duly declared in GSTR-3B of August 2019 but at a lesser value of Rs. 3,76,215.98 under Cess.
3. Section 39(9) read with Circular 26/26 also provides for rectification of errors/ omission:-
(9) Where any registered person after furnishing a return under sub-section (1) or sub-section (2) or sub-section (3) or sub-section (4) or sub-section (5) discovers any omission or incorrect particulars therein, other than as a result of scrutiny, audit, inspection or enforcement activity by the tax authorities, he shall rectify such omission or incorrect particulars in such form and manner as may be perscribed, subject to payment of interest under this Act:
Provided that no such rectification of any omission or incorrect particulars shall be allowed after the thirtieth day of Novemberfollowing the end of the financial year to which such details pertain, or the actual date of furnishing of relevant annual return, whichever is earlier.
In this case, above rectification has been done in September 2020 also. Hence, it is not a case where supply was not declared in the return, but only a case where the supply was incorrectly declared and later rectified under section 39(9).
4. No new supply was declared in September 2020 pertaining to August 2019 as all the supplies made in August 2019 was already declared in GSTR-1 (and GSTR-3B as well) and only a rectification of the same is done in September 2020
Therefore. on the above grounds you can argue that you are covered within proviso to section 50(1) and you need to pay interest on cash portion payable.