Nobody knows GAU Numbers
SOGL V0.12, 11 10 8 7 5 bytes
∫∫l*+

Try it Here! - this expects to be called as a function with the input on the stack and the input box empty.
7 byte alternative taking the input from the input box:
0.∫∫l*+

Try it Here!
0      push 0
 .     push the input
  ∫    iterate over a range 1..POP (input) inclusive, pusing the current number
   ∫    iterate over 1..POP (above loops number) inclusive, pusing the current number
    l    push that numbers length without popping the number
     *   multiply the length by the number
      +  add to the zero, or whatever it is now