\(2^{3x+3}-8^x=56\)
\(\Rightarrow2^{3x+3}-\left(2^3\right)^x=56\)
\(\Rightarrow2^{3x+3}-2^{3x}=56\)
\(\Rightarrow2^{3x}\left(2^3-1\right)=56\)
\(\Rightarrow2^{3x}\cdot7=56\)
\(\Rightarrow2^{3x}=56:7\)
\(\Rightarrow2^{3x}=8\)
\(\Rightarrow2^{3x}=2^3\)
\(\Rightarrow3x=3\)
\(\Rightarrow x=1\)