500 can be cubed and, sure as anything, is going to be bigger than 400.
How about 8 cubed = 512
6 and 7 are two whole integers that come to mind.
If you start with 401, then the answer to 401^3 is sure to be bigger than 400.
8 cubed is 512 - which meets the conditions of the question. Of course if you don't restrict it to integers, any number from about 7.368 to about 8.434 will also meet the conditions.
20 cubed ya is 400 ya
as i calculate it its 346, its the only cube number that's bigger than 200 but smaller than 400
400
it is 343
21 and 22
500
There is no number that is both smaller than 400 and larger than 600 - if it is smaller than 400 then it must be smaller than 600 since 400 is smaller than 600, similarly if it is larger than 600 then it must be larger than 400 since 600 is larger than 400. Assuming you mean larger than 400 and smaller than 600, then there are 199 such whole numbers than you can cube: 401, 402, 403, ..., 599 can all be cubed, giving 64481201, 64964808, 65450827, ..., 214921799. I guess that the question you are really asking is: What number between 400 and 600 is a perfect cube? The answer is 8³ = 512.
18 and 19