Parallelogram a Number
MATL, 12 bytes
tnEXyPY+c!Us

Input is a string. Try it online!
Explanation
Consider input '123' as an example.
The code duplicates the input (t) and builds an identity matrix (Xy) of size twice the input length (nE):
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1

then flips it upside down (P):
0 0 0 0 0 1
0 0 0 0 1 0
0 0 0 1 0 0
0 0 1 0 0 0
0 1 0 0 0 0
1 0 0 0 0 0

The input string, interpreted as ASCII codes of the digits, is equivalent to the numeric row vector
49 50 51

Full-size two-dimensional convolution (Y+) of the above vector and matrix gives
 0  0  0  0  0 49 50 51
 0  0  0  0 49 50 51  0
 0  0  0 49 50 51  0  0
 0  0 49 50 51  0  0  0
 0 49 50 51  0  0  0  0
49 50 51  0  0  0  0  0

Interpreting those numbers back as ASCII codes (c) gives the following char matrix, with char 0 represented as space:
     123
    123 
   123  
  123   
 123    
123

Transposition (!) transforms this into
     1
    12
   123
  123 
 123  
123   
23    
3     

Interpreting each row as a number (U) gives the numeric column vector
  1
 12
123
123
123
123
 23
  3

and summing it (s) gives the final result, 531.