So as all sides are equal in a cube, all the sides must be 7 as 7x7x7=343.
Then I think you will have to use Pythagoras at some point to work this out as to find the size of the longest stick that can fit in the box you will have to find out the length of the diagonal bit inside the cube. However, I don't know if this is right because have you learned about Pythagoras yet. Also, this is harder to explain without drawing it out. I hope this helps slightly.