Let's simplify the expression \( (x-y)^3 - (x+y)^3 (x-y)^3 - (x+y)^3 \).

First, we can rewrite the expression for clarity:

\[
(x-y)^3 - (x+y)^3 (x-y)^3 - (x+y)^3
\]

This can be grouped as:

\[
(x-y)^3 - (x+y)^3 ((x-y)^3 + 1)
\]

Next, let's calculate \( (x+y)^3 ((x-y)^3 + 1) \):

1. To expand \( (x+y)^3 \):
\[
(x+y)^3 = x^3 + 3x^2y + 3xy^2 + y^3
\]

2. To expand \( (x-y)^3 \):
\[
(x-y)^3 = x^3 - 3x^2y + 3xy^2 - y^3
\]

Now combining \( (x-y)^3 + 1 \):
\[
(x-y)^3 + 1 = (x^3 - 3x^2y + 3xy^2 - y^3) + 1
\]

Thus, \( (x+y)^3 ((x-y)^3 + 1) \) would involve distributing \( (x+y)^3 \) through \( (x-y)^3 + 1 \).

Next, we focus on the original expression and simplify as much as we can without expanding everything:

Let’s first compute our terms:
Using the identity \( a^3 - b^3 = (a-b)(a^2 + ab + b^2) \), we can analyze if this could apply to our problem as there are two cubes being subtracted.

Let \( a = (x-y) \) and \( b = (x+y)(x-y) \).

This leads us to analyze how they relate in terms of factoring.

After factoring through algebraic identities or expanding as previously mentioned, after all simplifications, we find intersections or symmetrical cancellations.

However, unless specific numeric values or further definition are provided, the expression remains:
\[
- (x+y)^3 \left( (x-y)^3 + 1 \right) + (x-y)^3
\]

This does not seem to simplify further into simple terms of \( x \) and \( y \) without being overly complex and does not lead to any reduction beyond polynomial format.

Thus, the original expression, depending on the values of \( x \) and \( y \), simplifies down to this cubic relation.

If we input specific values for \( x \) and \( y \), we can find numerical simplifications or reductions to simple forms; however, algebraically this is the concise representation.