7. It is known that the four-digit number $\overline{A B C D}$ satisfies the following property: $\overline{A B} 、 \overline{B C} 、 \overline{C D}$ are all perfect squares (a perfect square is a number that can be expressed as the square of an integer, for example, $4=2^{2}, 81=9^{2}$, so we call $4 、 81$ perfect squares). The sum of all four-digit numbers that satisfy this property is $\qquad$ .
【Analysis】The square numbers that satisfy the conditions are:
$$
\begin{array}{rlr}
\overline{A B} & \overline{B C} & \overline{C D} \\
16 & 64 & 49 \\
36 & 64 & 49 \\
81 & 16 & 64 \\
\therefore \overline{A B C D}=1649 \text { or } 3649 \text { or } 8764 & & \\
\therefore \text { The sum is } 1649+3649+8764=13462 &
\end{array}
$$