Factor x³ + 8.

We have a sum of cubes. Luckily, they're regular math cubes, not gelatinous cubes. Those things are nasty, with a capital "Arg, I'm melting!"

(x)³ + (2)³

According to our general formula, this factors to a binomial that shares its sign with the sum, and has the opposite sign inside the trinomial.

(x + 2)(x² – 2x + 4)

It looks a lot like that, yep.

Factor x³ – 343.

Is 343 a cube? Hold on while we grab a calculator…oh, yeah, it's 7³. We can work with that, then. It will factor to:

(x – 7)(x² + 7x + 49)

Factor 27x³ – 64y³.

A little bit of rewriting gets us:

(3x)³ – (4y)³

This difference between two cubes transforms into:

(3x – 4y)[(3x)² + (3x)(4y) + (4y)²]

A little bit of pruning will make this look nicer.

(3x – 4y)(9x² + 12xy + 16y²)

Factor a⁹ + b⁶.

(a³)³ + (b²)³

We put an exponent in your exponent, so you can raise to a power while raising to a power.

(a³ + b²)[(a³)² – a³b² + (b²)²]

Simplify it out, while being careful not to mess up the exponents. They'll multiply together in this case.

(a³ + b²)(a⁶ – a³b² + b⁴)