How to factorise a raised to 6 + b raised to 6

Use the calculator on this site:

$${factor}{\left({{\mathtt{a}}}^{{\mathtt{6}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{b}}}^{{\mathtt{6}}}\right)} = \left({{\mathtt{b}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{a}}}^{{\mathtt{2}}}\right){\mathtt{\,\times\,}}\left({{\mathtt{b}}}^{{\mathtt{4}}}{\mathtt{\,-\,}}{{\mathtt{a}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{{\mathtt{b}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{a}}}^{{\mathtt{4}}}\right)$$

You can't.

Think about it.

a^6 + b^6 = a*a*a*a*a*a + b*b*b*b*b*b

It's not that obvious. For example,

$$a^{7}+b^{7}=(a+b)(a^{6}-a^{5}b+a^{4}b^{2}-a^{3}b^{3}+a^{2}b^{4}-ab^{5}+b^{6}).$$