Task B-2.5. What is the last digit of the number $2012^{3}+3^{2012}$?
Solution. The number $2012^{3}$ ends with the digit 8.

The powers of the number $3, 3^{1}, 3^{2}, 3^{3}, 3^{4}, 3^{5}, 3^{6}, \ldots$ end with the digits $3,9,7,1,3,9, \ldots$,

that is, every fourth digit repeats.

Therefore, the number $3^{2012}=\left(3^{4}\right)^{503}$ has the same units digit as the number $3^{4}$, which is the number 1.

Since $8+1=9$, the number $2012^{3}+3^{2012}$ ends with the digit 9.