3. The maximum number of parts that space can be divided into by $n$ planes is
$\qquad$ parts.
3. Solution: Let the maximum number of parts be $a_{n}$, then when adding the $(n+1)$-th plane, it intersects with the previous $n$ planes to form $n$ intersection lines. These $n$ lines divide the $(n+1)$-th plane into $\frac{n(n+1)}{2}+1$ parts, and each part divides the space it is in into two parts, thus increasing the number of parts by $\frac{n(n+1)}{2}+1$. Therefore, we have $a_{n+1}=a_{n}+\frac{n(n+1)}{2}+1=a_{n}+\mathrm{C}_{n+1}^{2}+1, a_{1}=2$.
$$
\begin{array}{l}
a_{n}=a_{n}-a_{n-1}+a_{n-1}-a_{n-2}+\cdots+a_{2}-a_{1}+a_{1} \\
=\mathrm{C}_{2}^{2}+\mathrm{C}_{3}^{2}+\cdots+\mathrm{C}_{n}^{2}+(n-1)+2=\mathrm{C}_{n+1}^{3}+n+1 \\
=\frac{n^{3}+5 n+6}{6} .
\end{array}
$$