Hey guys..I'm having trouble factoring some functions...I can pretty easily factor and find the solutions for linear and quadratic functions, but when it comes to cubic and..um..higher-powered functions, I'm pretty lost...

The first problem is:

x^3 + 216 = 0

I know to start I should set 216 to its cubic form,

x^3 + 6^3 = 0, but I have no idea what to do after that...

make use of the sum of cubes formula!
And for the next problem I have

x^4 - x^3 + x - 1 = 0

I worked it out like this:

x^3(x - 1) + 1 (x - 1 )= 0

(x^3+1) (x-1) = 0

so I solve for x

x^3 + 1 = 0

(no solution) and

What's (-1)^3?!
x-1 = 0

x=1....but the answer says its x = + or - 1...So I definitely did something wrong...

So if anyone could help me I'd greatly appreciate it