To analyze the expression \( D = 2(x^3 + y^3) - 3(x^2 + y^2) \) under the constraint \( x + y = 1 \), we can express \( y \) in terms of \( x \):

\[
y = 1 - x.
\]

We can substitute this into our expression for \( D \):

1. First, calculate \( x^2 + y^2 \):
\[
y^2 = (1-x)^2 = 1 - 2x + x^2,
\]
\[
x^2 + y^2 = x^2 + (1 - 2x + x^2) = 2x^2 - 2x + 1.
\]

2. Next, calculate \( x^3 + y^3 \):
\[
y^3 = (1-x)^3 = 1 - 3x + 3x^2 - x^3,
\]
\[
x^3 + y^3 = x^3 + (1 - 3x + 3x^2 - x^3) = 1 - 3x + 3x^2.
\]

Now substitute these two results back into the equation for \( D \):

\[
D = 2(1 - 3x + 3x^2) - 3(2x^2 - 2x + 1).
\]

Let's simplify this step by step:

\[
D = 2 - 6x + 6x^2 - 6x^2 + 6x - 3.
\]

Combine like terms:

\[
D = (2 - 3) + (-6x + 6x) + (6x^2 - 6x^2),
\]
\[
D = -1.
\]

Since \( D \) simplifies to \(-1\) and does not depend on \( x \), it is constant under the constraint \( x + y = 1 \).

Thus, the final result is

\[
D = -1 \quad \text{when } x + y = 1.
\]