Factorise -a^6+8b^6+c^6+ 6a^2 b^2 c^2
Not sure that this is any easier to read, but I get
(-a^2+b^2+c^2)(a^4+2a^2b^2+a^2c^2+4b^4-2b^2c^2+c^4)
to get there, note that the second factor is
(b^2+a^2)^2 + (b^2+b^2)^2 + (b^2-c^2)^2
(-a^2+b^2+c^2)(a^4+2a^2b^2+a^2c^2+4b^4-2b^2c^2+c^4)
to get there, note that the second factor is
(b^2+a^2)^2 + (b^2+b^2)^2 + (b^2-c^2)^2