2. $1^{2}, 2^{2}, 3^{2}, \cdots, 123456789^{2}$ The unit digit of the sum is $\qquad$ .
2. 5

Solution: Since $123456789=10 \times 12345678+9$,
the required digit is equal to
$$
(1+4+9+6+5+6+9+4+1+0) \times 12345678
$$
$+(1+4+9+6+5+6+9+4+1)$, which is the unit digit of $5 \times 8+5=45$, so the required digit is 5.