The new vol = 8 times the old vol. Therefore the sides of the cube have been made 2 times larger. (the cube root of 8 is 2.)
Doubled: Volume increased 8 times
Tripled: Volume increased 27 times
Quadrupled: Volume increased 64 times
Pretty simple. If you're doubling the lengths, you're increasing them by 2 times. Take 2 and raise it to the 3rd power. If you're tripling the lengths, you're increasing them 3 times over. Take 3 and raise it to the 3rd power. And so on.
Doubled = 2^3 = 8
Tripled = 3^3 = 27
Quadrupled = 4^3 = 64
Does that make sense?