Start the solution by pronouncing the standard phrase: let x be the side of the cube.


Then you write equation for the volume of the extended solid body as you read the problem


    x*(x+2)*(x+2) = 245  cubic cm.


Here  " x "   is unchangeable height of the original cube.



Although this equation is cubical, it is not difficult to solve it mentally in your head

    (and the entire problem is designed and constructed 
     in order for this easy mental solution would be possible).



First, we will try integer numbers for x.
Second, these numbers should not be great: they definitely less than 10.
Third, one of the factors in equation (*) must be 5 (OBVIOUSLY).


Let's try x = 5.  Then your product is  5*(5+2)*(5+2) = 5*7*7 = 5*49 = 245, so x= 5 is the solution.


In addition, you may note that the volume function  x*(x+2)*(x+2)  is monotonically increasing;

THEREFORE, x= 5 is a UNIQUE solution in real numbers.


ANSWER.  The original dimensions of the cube were 5 x 5 x 5 centimeters,