Example 6 Find the unit digit of the sum $1^{2}+2^{2}+3^{2}+4^{2}+\cdots+1994^{2}$.
Solution: Since this problem only requires the unit digit of the sum, we only need to consider the unit digit of each number. Thus, the original problem simplifies to finding the unit digit of
$$
\underbrace{i^{2}+2^{2}+3^{2}+4^{2}+\cdots+9^{2}}_{\text {199 groups }}+1^{2}+2^{2}+3^{2}+4^{2}
$$

The unit digits follow a periodic pattern:
$$
1,4,9,6,5,6,9,4,1 \text {, }
$$

The unit digit of the sum of each group is 5, so the unit digit of the sum of 199 groups is also 5. Considering the unit digit sum of the remaining four numbers is 0, the unit digit of the required sum is 5.