You seem to be confusing a lot of things. First of all an array in C# or any other language is referring to a data structure which stores values of certain type like integers, doubles, string etc. This is the representation of data not a rendering of a three dimensional object.
It is correct that a multidimensional array in C# cannot be resized once declared. You would need to declare a new array and copy the elements.
If you treat that 3D array like a cube, you can indeed update certain "slices". The smallest part an array consists of are the elements which can be accessed through their index. You can imagine them as boxes that store content and each have numbers identifying them. For a 3D array, that would be three numbers one for each dimension.
To update what you called a slice you would iterate through all boxes in two dimensions and keep the third fixed. As the 3D is only an abstraction there actually is no side you are facing when treating it figuratively as a thing.
For actual 3D rendering of cubes, which are not the same thing as an array, you might want to check out OpenGL, XNA Game or 3D rendering with WPF.
I hope that clarifies things a little.
Here is a tutorial on how to use arrays, should be simple enough to follow along for a beginner.
As for 3D rendering with C# I am not a great help, because I have never done it myself. But there are plenty tutorials for that as well. For example this.