1.12: this is the sum $1200^3 + 1^3$.

1.13: You can assume $a\geq b\geq c$ without loss of generality.

1.15: The last digit is $2$.  If you multiply this number by $2$, the last digit $2$ is moved to the first digit.  With this information, you can simply carry out the multiplication on paper, until the first digit of the result is $2$.  This number has more than 10 digits.

1.16: Consider pairing and symmetry.