70大庆

$$\begin{align}\quad & 1^2+2^2+3^2+4^2+\cdots+24^2\\
=& 1\times(2-1)+2\times(3-1)+3\times(4-1)+4\times(5-1)+\cdots+24\times(25-1)\\
=& 1\times2-1+2\times3-2+3\times4-3+4\times5-4+\cdots+24\times25-24\\
=& 1\times2+2\times3+3\times4+4\times5+\cdots+24\times25-(1+2+3+4+\cdots+24)\\
=& 24\times25\times26\div3-(1+24)\times24\div2\\
=& 24\times25\times49\div6\\
=& 70^2\\
\end{align}$$