Expanding the given expression, we get:

2(x^2 - 2x + 1) + (x^3 - x^2 + x + x^2 - x + 1) - (x^3 + 3x^2 + 3x + 1)

Now simplify by combining like terms:

2x^2 - 4x + 2 + x^3 - x^3 + 2x - 2x + x - x - 1 - x^3 - 3x^2 - 3x - 1

2x^2 - 4x + 2 + 2x - 2x + x - x - 1 - 3x - 1

2x^2 - 5x - 2

Therefore, the simplified form of the expression 2(x-1)^2 + (x+1)(x^2-x+1) - (x+1)^3 is 2x^2 - 5x - 2.