1. Domain of definition (ODZ) $x>-2 ; x \neq-1$

$$
\log _{2+x}\left(8+x^{3}\right) \leq \log _{2+x}(2+x)^{3} \Leftrightarrow\left(8+x^{3}-(2+x)^{3}\right)(2+x-1) \leq 0 \Leftrightarrow x(x+2)(x+1) \leq 0 \Rightarrow
$$
Answer: $-2<x<-1 ; x \geq 0$