This problem is asking you to think backward about a mathematical problem that you already know how to solve.
The first thing you should do when faced with a problem where you don't know "the answer" is to think about what you do know.
In this case, what can you tell me about the volume of a cube?
Since we know that the volume of a cube is the the cube of its side length (or, more generally: the volume of a rectangular block is length times width times height; or even more generally: the volume of any cylinder is base area times height) we can proceed to writing down an equation for the problem.
In this case V=L3=27
The question can now be rephrased as, what is the cube root of 27? Or, if you prefer, less formally, as what number cubed equals 27?
33=27 so we have our answer that the length of the sides of the cube is 3.
I hope that helps you not only get the right answer, but see some strategies for solving other problems in mathematics as well!