$\begin{array}{l}
Bai\,\,5:\,\,\,a,\,\,b,\,\,c\,\,\,la\,\,\,3\,\,so\,\,nguyen\,\,lien\,\,tiep\\
\Rightarrow cac\,\,so\,\,la:\,\,\,n,\,\,n + 1,\,\,n + 2\,\,\,\,\,\left( {n \in Z} \right).\\
\Rightarrow {a^3} + {b^3} + {c^3} = {n^3} + {\left( {n + 1} \right)^3} + {\left( {n + 2} \right)^3}\\
= {n^3} + {n^3} + 3{n^2} + 3n + 1 + {n^3} + 6{n^2} + 12n + 8\\
= 3{n^3} + 9{n^2} + 15n + 9\\
= 3\left( {{n^3} + 3{n^2} + 5n + 3} \right)\,\, \vdots \,\,\,3\,\,\,\left( {dpcm} \right).
\end{array}$
