6.022. $(x+3)^{3}-(x+1)^{3}=56$.

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6.022. $(x+3)^{3}-(x+1)^{3}=56$.
## Solution.

Domain: $x \in R$.

From the condition we have

$$
\begin{aligned}
& (x+3-x-1)\left((x+3)^{2}+(x+3)(x+1)+(x+1)^{2}\right)=56 \Leftrightarrow \\
& \Leftrightarrow 2\left(x^{2}+6 x+9+x^{2}+4 x+3+x^{2}+2 x+1\right)=56 \Leftrightarrow \\
& \Leftrightarrow x^{2}+4 x-5=0, x_{1}=-5, x_{2}=1
\end{aligned}
$$

Answer: $x_{1}=-5, x_{2}=1$.