.......In the 1981 original motion picture, "The Cannonball Run",  JJ
(Burt Reynolds) stops for fuel and Victor (Dom DeLuise) runs into a
store to buy some needed race essentials.  Upon exit from the store
Victor shuffles, struts, dances and sings while sipping his purchase.
 
What is the specific name of the store, brand of refreshment and drink
cup description Victor purchased?

7-Eleven stores had a promotional tie-in with this movie. The drink
was a 7-Eleven "Big Gulp" Dr Pepper. So your answer is:

Store: 7-Eleven
Brand of Refreshment: Dr Pepper
Drink Cup Description: Big Gulp

"I remember buying my first Big Gulp at Seven-11 in 1981. It came in a
'Cannonball Run' collectors cup."

Comic Book Resources Forums
http://forums.comicbookresources.com/archive/index.php/t-23298.html

"Victor, what do you got? 

A lot of goodies for you guys, and a Big Gulp Dr. Pepper for me.
(singing) I'm a Pepper, you're a Pepper, he's a Pepper, wouldn't you
like to be a Pepper too!...

Cannonball Run, The - 1981" 

Movie Quotes
http://www.moviequotes.com/fullquote.cgi?qnum=3826

"The product placement reaches outrageous proportions, to the extent
of DeLuise singing the Dr. Pepper theme song. Budweiser and 7-11 also
get huge amounts of exposure, which is the one point that really
detracts from enjoyment of the movie."

Digitally Obsessed: The Cannonball Run
http://www.digitallyobsessed.com/showreview.php3?ID=1348

Google search strategy:

Google Web Search: "cannonball run" + "dr pepper"
://www.google.com/search?hl=en&q=%22cannonball+run%22+%22dr+pepper%22

I hope this is helpful! If anything is unclear or incomplete, please
request clarification; I'll be glad to offer further assistance before
you rate my answer.

Best regards,
pinkfreud

Thank you!