In my comment I've been referencing https://arxiv.org/pdf/2005.14165.pdf, specifically section 3.9.1 where they summarize results of the arithmetic tasks.

Check out this one: https://thegradient.pub/othello/

In it, researchers built a custom LLM trained to play a board game just by predicting the next move in a series of moves, with no input at all about the game state. They found evidence of an internal representation of the current game state, although the model had never been told what that game state looks like.

GPT3 is pretty bad at it compared to alternatives (although it's hard to compete with calculators on that field), but if it was just repeating after the training dataset it would be way worse. From the study I've linked in my other comment (https://arxiv.org/pdf/2005.14165.pdf):

On addition and subtraction, GPT-3 displays strong proficiency when the number of digits is small, achieving 100% accuracy on 2 digit addition, 98.9% at 2 digit subtraction, 80.2% at 3 digit addition, and 94.2% at 3-digit subtraction. Performance decreases as the number of digits increases, but GPT-3 still achieves 25-26% accuracy on four digit operations and 9-10% accuracy on five digit operations, suggesting at least some capacity to generalize to larger numbers of digits.

To spot-check whether the model is simply memorizing specific arithmetic problems, we took the 3-digit arithmetic problems in our test set and searched for them in our training data in both the forms " + =" and " plus ". Out of 2,000 addition problems we found only 17 matches (0.8%) and out of 2,000 subtraction problems we found only 2 matches (0.1%), suggesting that only a trivial fraction of the correct answers could have been memorized. In addition, inspection of incorrect answers reveals that the model often makes mistakes such as not carrying a “1”, suggesting it is actually attempting to perform the relevant computation rather than memorizing a table.