One for the geniuses out there...

[A$$Bandit]

You are given only this information:

x + y + z = 4
x² + y² + z² = 6
xyz = 3

You are required to determine a numerical value for:

x³ + y³ + z³

No fancy stuff, just algebraic manipulation... I couldn't figure it out so anyone who can point me in the right direction, please relieve me of this.