Nope, the 6 in the VIN means it was a V-8 Bel Air sport coupe. 6 cyl would be 1537.....odd number is 6 cyl, even number for 8.
A 6 cyl car would still show 1637 on the trim tag but would be 1537 on the VIN.
your correct
Chevrolet 1960 - 1964
1st digit - Model year. (0) 1960, (1) 1961, (2) 1962, (3) 1963, (4) 1964 2nd and 3rd digit - Series. (11) Biscayne L6, (12) Biscayne V8, (13) Biscayne Fleetmaster L6 (1960-61) or Impala SS L6 (1964), (14) Biscayne Fleetmaster V8 (1960-61) or Impala SS V8 (1964), (15) Bel Air L6,
(16) Bel Air V8, (17) Impala L6, (18) Impala V8 4th and 5th digits - Body style. (11) 2-door sedan, (15) 2-door wagon, (19) 4-door sedan, (21) 2-door Utility sedan, (35) 4-door wagon (6-passenger), (37) 2-door Sport coupe (bubble top), (39) 4-door Sport sedan, (45) 4-door wagon (9-passenger), (47) 2-door Sport coupe, (67) 2-door convertible, (69) 4-door sedan 6th digit - Assembly plant. (A) Atlanta, GA, (B) Baltimore, MD, (F) Flint, MI, (G) Pontiac, MI, (H) Fremont, CA, (J) Janesville, WI, (K) Kansas City, MO, (L) Los Angeles, CA, (N) Norwood, OH, (O) Oakland, CA, (R) Arlington, TX, (S) St. Louis, MO, (T) Tarrytown, NY, (U) Southgate, CA,