To compute $987654321^2$, we can write $987654321$ as $10^9 - 12345679$. Then, we can compute $(10^9 - 12345679)^2$:
$$ (10^9 - 12345679)^2 = (10^9)^2 - 2(10^9)(12345679) + (12345679)^2 $$
$$ = 10^{18} - 24691358 \cdot 10^9 + (12345679)^2 $$
$$ = 10^{18} - 24691358000000000 + (12345679)^2 $$
Let's compute $12345679^2$:
$$ 12345679 \times 12345679 = 152415787501905 $$
Then,
$$ 10^{18} - 24691358000000000 + 152415787501905 $$
$$ = 1000000000000000000 - 24691358000000000 + 152415787501905 $$
$$ = 975308642000000000 + 152415787501905 $$
$$ = 975308641999999999 + 152415787501906 $$
$$ = 975308641999999999 + 152415787501905 = 975308641999999999 + 152415787501905 $$
Let's use a different approach.
Let $x = 987654321$. Then $x = 987654300 + 21$. We know $987654321^2 = (987654300+21)^2 = 987654300^2 + 2(987654300)(21) + 21^2$
$= 987654300^2 + 41477688600 + 441$
$= 9754610577690000 + 41477688600 + 441$
$= 9754610577690000 + 41477689041 = 9755025354580441$

We can compute the square of $987654321$ by expanding it:
$$\begin{array}{@{}c@{\,}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c@{}c}
& & & & & & & 9 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 \\
& & & & & & \times & 9 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 \\
\hline
& & & & & & & 9 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 \\
& & & & & & 1 & 9 & 7 & 5 & 3 & 0 & 8 & 6 & 4 & 2 & 0 \\
& & & & & 2 & 9 & 6 & 2 & 9 & 6 & 2 & 9 & 8 & 6 & 0 & 0 \\
& & & & 3 & 9 & 5 & 0 & 6 & 1 & 7 & 2 & 9 & 2 & 0 & 0 & 0 \\
& & & 4 & 9 & 3 & 8 & 2 & 6 & 4 & 8 & 6 & 4 & 0 & 0 & 0 & 0 \\
& & 5 & 9 & 2 & 5 & 9 & 1 & 8 & 4 & 9 & 2 & 0 & 0 & 0 & 0 & 0 \\
& 6 & 9 & 1 & 3 & 5 & 8 & 0 & 1 & 5 & 4 & 8 & 0 & 0 & 0 & 0 & 0 \\
7 & 9 & 0 & 1 & 2 & 3 & 2 & 5 & 8 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
8 & 8 & 8 & 8 & 8 & 8 & 9 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
\hline
9 & 7 & 5 & 4 & 6 & 1 & 0 & 5 & 7 & 7 & 6 & 9 & 0 & 0 & 0 & 0 & 0 \\
\end{array}$$
The correct result is $975461057769000000 + 197530864200000 + 296296298600 + 3950617292000 + 49382716486400 + 5925925918492000 + 69135801548800000 + 790123258000000000 + 888888888900000000 = 975308642000000000$, then we need to sum
The correct result is 975461057769000000 + 41477689041 = 97546109924689041

Final Answer: The final answer is $\boxed{97546105776904141}$
