I think cmp -l file1 file2 might do what you want. From the manpage:

-l  --verbose
      Output byte numbers and values of all differing bytes.

The output is a table of the offset, the byte value in file1 and the value in file2 for all differing bytes. It looks like this:

4531  66  63
4532  63  65
4533  64  67
4580  72  40
4581  40  55
[...]

So the first difference is at offset 4531, where file1's decimal byte value is 66 and file2's is 63.

I think cmp -l file1 file2 might do what you want. From the manpage:

-l  --verbose
      Output byte numbers and values of all differing bytes.

The output is a table of the offset, the byte value in file1 and the value in file2 for all differing bytes. It looks like this:

4531  66  63
4532  63  65
4533  64  67
4580  72  40
4581  40  55
[...]

So the first difference is at offset 4531, where file1's decimal octal byte value is 66 and file2's is 63.