In Excel, the columns are identified by
a b c .... z aa ab ac .... az ba bb bc .... yz za zb zc .... zz aaa aab aac ....

These identifications correspond to the numerical values as
1 2 3 .... 26 27 28 29 .... 52 53 54 55 .... 676 677 678 679 .... 702 703 704 705 ....

How to write a C++ code that can perform the bilateral conversion between these two different identification schemes?

Think of each letter of the alphabet as a number from 1-26. So a-z are just 1 thru 26. And aa = 1x26 + 1, ab = 1x 26 + 2, etc. zz = 26x26+26 = 702, aaa = (1x26x26)+(1x26)+1 = 703. So basically you would just parse the digits and do the conversion. It's not really a "base" per se as there are no a0,a1,a2, etc in between z and aa.

After all that, though I think there is a setting in Excel where you can change your column headings to be column number instead of this system.