an element of $(A\times B)\times(C\times D)$ is of the form
$$ \Big((a,b),(c,d)\Big) $$
Because "$\times$" is a binary operation on sets, $A\times(B\times C)\times D$ doesn't make sense UNLESS you defined it as ordered triples; in which case an element is of the form
$$\Big(a,(b,c),d\Big)$$
There is a one-to-one onto function from one set to the other however. Namely
$$ \Big((a,b),(c,d)\Big)\mapsto \Big(a,(b,c),d\Big) $$
Recall $(a,b)$ is notation for $\{\{a\},\{a,b\}\}$.
Following Endertons' Elements of Set Theory textbook, $n$-tuples are defined as follows
$$ (x,y,z)\overset{\mathrm{def}}{=} ((x,y),z) $$
$$ (x,y,z,u)\overset{\mathrm{def}}{=} ((x,y,z),u) $$
$$\vdots$$