How can I create a cubic sphere ?

I’d like to create a cubic sphere that looks somewhat similar to this style:

Taking into considering I’m new to Unity, should I use Dynamic Mesh, Mesh class or perhaps some procedure with Blender ?

There are several ways to do it.

  1. create a black&white texture and use it as a height-map in shader to displace the vertices of original sphere.

  2. as @Guhanesh said use a modeling software to create mesh and you can use vertex color to animate heights of cube from shader.

  3. procedural mesh generation, the most complex way. I never created cubic sphere before but i can give you some pseudo code:
    ->devide sphere in longitude and latitude that will give you array of points on sphere equally spaced.
    → use this points as center of face of cubes and get 4 vertex position around it, now create two triangles to make a complete square face.
    → you also have to create side faces of that square to make a complete cube.
    → after all of this if you have a mesh its not over yet, to create UV map, calculate UV for each vertex in the mesh. this will allow you to apply some texture on cubic-sphere.