We can easily test the commutativity of a binary operation on a set of $\ n\in\mathbb{N}\ $ elements by observing the symmetry of the $\ n\times n\ $ multiplication table.

I was looking for a similar test for the associativity of a binary operation. Since it should work on "triples", I don't expect to find anything in a square table.

I tried with a $\ n\times n\times n\ $ table, only in the case of binary operations on a set of two elements (I can only use a pencil), and it turned out that there are cubic tables for associative operations equal to cubic tables for non-associative operations.

So, do you happen to know a "model" to represent a binary operation from which it is clearly visible the associativity of the operation? Thanks!