Can you factor (t³-8)? 

Yes, it's the difference of two cubes, t³ - 2³

It can be divided by t - 2.

We first write t³ - 8 as t³ + 0t² + 0t - 8

              t² + 2t + 4  
  t - 2)t³ + 0t² + 0t - 8
        t³ - 2t²
             2t² + 0t
             2t² - 4t
                   4t - 8
                   4t - 8
                        0

That means t³ - 2³ factors as (t - 2)(t² + 2t + 4)

To save having to do long division every time, memorize
this:

A³ + B³ factors as (A + B)(A - AB + B²)

and

A³ - B³ factors as (A - B)(A + AB + B²)

Edwin