Divide a large cube into 125 smaller cubes of equal size?

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Could somebody please tell me how can one divide a large cube into 125 smaller cubes of equal size? I can very well understand i can divide a large cube into 225 smaller cubes because 15*15=225. I just HAVE NO ideas. You?
 
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I am just guessing, but if a large cube is 5*5*5, would not that cube store 125 smal cubes on 1*1*1?
 


Oh, yes, 5*5*5 would be 125. You're right. Thank you. I just forgot its a cube, not a square! :)
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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