1. (10 points) Calculate: $(2014 \times 2014 + 2012) - 2013 \times 2013$
【Analysis】Consider 2014 as 2013+1, and 2012 as 2013-1, and simplify the calculation accordingly.
$$
\begin{array}{l}
\text { 【Solution】Solution: }(2014 \times 2014+2012)-2013 \times 2013 \\
=[(2013+1) \times(2013+1)+(2013-1)]-2013 \times 2013 \\
=(2013+1) \times(2013+1)+2013-1-2013 \times 2013 \\
=2013 \times 2013+2013+2013+1+2013-1-2013 \times 2013 \\
=(2013 \times 2013-2013 \times 2013)+(1-1)+(2013+2013+1+2013) \\
=6039 .
\end{array}
$$

Therefore, the answer is: 6039.