Answer
By a factor of $27$.
Work Step by Step
The volume $V$ of a cube is given by the formula $V = s^3$ where $s$ and the length of a side.
The volume of the original cube is $V=x^3$.
If the side length is changed to $3x$, then the volume of the bigger cube is $V=(3x)^3=(3x)(3x)(3x)=27x^3$
Thus, the change is by a factor of $\dfrac{27x^3}{x^3} = 27$.
