6.215. $\left\{\begin{array}{l}x^{3}+3 x y^{2}=158 \\ 3 x^{2} y+y^{3}=-185 .\end{array}\right.$
Solution.

Add and subtract the first and second equations:

$$
\begin{aligned}
& \left\{\begin{array} { l } 
{ x ^ { 3 } + 3 x y ^ { 2 } + 3 x ^ { 2 } y + y ^ { 3 } = - 2 7 , } \\
{ x ^ { 3 } + 3 x y ^ { 2 } - 3 x ^ { 2 } y - y ^ { 3 } = 3 4 3 }
\end{array} \Leftrightarrow \left\{\begin{array}{l}
(x+y)^{3}=-27, \\
(x-y)^{3}=343
\end{array} \Leftrightarrow\right.\right. \\
& \Leftrightarrow\left\{\begin{array} { l } 
{ x + y = - 3 , } \\
{ x - y = 7 }
\end{array} \Leftrightarrow \left\{\begin{array}{l}
x=2 \\
y=-5
\end{array}\right.\right.
\end{aligned}
$$

Answer: $(2, -5)$.