For something I want to do with these cubes I need to create the mesh myself so I know which vertices are which and am able to manipulate the geometry.

But why does my scripted cube (on the left) look so different in shading than the Unity one?

Both use the same material.

I guess it has something to do with the Phong?

This is the code I use to create my own cube:

private void CreateCube() 
{

    GameObject cubeObject;
    cubeObject = Instantiate(prefab, new Vector3(0, 0, 0), Quaternion.identity);

    Vector3[] vertices;
    int[] triangles;

    vertices = new Vector3[8];

    // BOTTOM VERTICES
    vertices[0] = new Vector3(0, 0, 0); //BBL
    vertices[1] = new Vector3(1, 0, 0); //BBR
    vertices[2] = new Vector3(0, 0, 1); //BTL
    vertices[3] = new Vector3(1, 0, 1); //BTR
    // TOP VERTICES
    vertices[4] = new Vector3(0, 1, 0); //TBL
    vertices[5] = new Vector3(1, 1, 0); //TBR
    vertices[6] = new Vector3(0, 1, 1); //TTL
    vertices[7] = new Vector3(1, 1, 1); //TTR

    triangles = new int[36];

    // BOTTOM TRIANGLES
    triangles[0] = 1; //BBR
    triangles[1] = 2; //BTL
    triangles[2] = 0; //BBL
    triangles[4] = 2; //BTL
    triangles[3] = 3; //BTR
    triangles[5] = 1; //BBR
    
    // TOP TRIANGLES
    triangles[6] = 4; //TBL
    triangles[7] = 6; //TTL
    triangles[8] = 7; //TTR
    triangles[9] = 5; //TBR
    triangles[10] = 4; //TBL
    triangles[11] = 7; //TTR

    // BACK TRIANGLES
    triangles[12] = 5; //TBR
    triangles[13] = 0; //BBL
    triangles[14] = 4; //TBL
    triangles[15] = 1; //BBR   
    triangles[16] = 0; //BBL
    triangles[17] = 5; //TBR

    // FRONT TRIANGLES
    triangles[18] = 6; //TTL
    triangles[19] = 2; //BTL
    triangles[20] = 3; //BTR
    triangles[21] = 6; //TTL
    triangles[22] = 3; //BTR 
    triangles[23] = 7; //TTR

    // LEFT TRIANGLES
    triangles[24] = 6; //TTL
    triangles[25] = 4; //TBL 
    triangles[26] = 2; //BTL
    triangles[27] = 0; //BBL 
    triangles[28] = 2; //BTL 
    triangles[29] = 4; //TBL 

    // RIGHT TRIANGLES
    triangles[32] = 7; //TTR
    triangles[31] = 5; //TBR
    triangles[30] = 1; //BBR  
    triangles[35] = 1; //BBR  
    triangles[34] = 3; //BTR 
    triangles[33] = 7; //TTR

    Mesh cubeMesh = new Mesh(); 

    cubeObject.GetComponent<MeshFilter>().sharedMesh = cubeMesh;

    cubeMesh.Clear();
    cubeMesh.vertices = vertices;
    cubeMesh.triangles = triangles;

    cubeMesh.RecalculateNormals();
}

The prefab is just a GameObject with an empty Mesh Filter and a Mesh Renderer with a material attached (Default-Material).