* Find all integer solutions $x$ of the equation $x^{3}+(x+1)^{3}+(x+2)^{3}=(x+3)^{3}$.
In the original equation, let $x=t+3$, we get the equation $2 t\left(t^{2}+3 t+21\right)=0$. It has only one real solution $t=0$, thus the original equation has only one integer solution $x=3$.

解析

In the original equation, let $x=t+3$, we get the equation $2 t\left(t^{2}+3 t+21\right)=0$. It has only one real solution $t=0$, thus the original equation has only one integer solution $x=3$.