7. A. For any real numbers $x, y$, define the operation
$$
x \oplus y=x+2 y+3 \text {. }
$$

It is known that real numbers $a, b$ satisfy
$$
\left(a^{3} \oplus a^{2}\right) \oplus a=a^{3} \oplus\left(a^{2} \oplus a\right)=b \text {. }
$$

Then $a+b=$ $\qquad$
7. A. $\frac{21}{8}$.

From the given, we have
$$
\begin{array}{l}
b=\left(a^{3} \oplus a^{2}\right) \oplus a \\
=\left(a^{3}+2 a^{2}+3\right)+2 a+3 \\
=a^{3}+2 a^{2}+2 a+6, \\
b=a^{3} \oplus\left(a^{2} \oplus a\right) \\
=a^{3}+2\left(a^{2}+2 a+3\right)+3 \\
=a^{3}+2 a^{2}+4 a+9 .
\end{array}
$$

Subtracting the two equations, we get
$$
2 a+3=0 \Rightarrow a=-\frac{3}{2} \text {. }
$$

Thus, $a+b=a+\left(a^{3}+2 a^{2}+2 a+6\right)$
$$
=a^{3}+6+a(2 a+3)=\frac{21}{8} \text {. }
$$