A cube mesh created with code including uv mapping mesh and normals

ProceduralCube.cs

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

[RequireComponent(typeof(MeshFilter))]
[RequireComponent(typeof(MeshRenderer))]
[ExecuteInEditMode] // Added to be able to tweak the script without having to hit play ever time
public class ProceduralCube : MonoBehaviour
{

    // size of the cube sides
    public float cubeSize = 0.2f;

    // hardcoded values for a single cube
    private static Vector3[] cubeVertices = new Vector3[]{
        // Front Side
        new Vector3(0f, 0f, 0f),
        new Vector3(1f, 0f, 0f),
        new Vector3(0f, 1f, 0f),
        new Vector3(1f, 1f, 0f),

        // Right Side
        new Vector3(1f, 0f, 0f),
        new Vector3(1f, 0f, 1f),
        new Vector3(1f, 1f, 0f),
        new Vector3(1f, 1f, 1f),

        // Back Side
        new Vector3(1f, 0f, 1f),
        new Vector3(0f, 0f, 1f),
        new Vector3(1f, 1f, 1f),
        new Vector3(0f, 1f, 1f),

        // Left Side
        new Vector3(0f, 1f, 0f),
        new Vector3(0f, 1f, 1f),
        new Vector3(0f, 0f, 0f),
        new Vector3(0f, 0f, 1f),

        // Top Side
        new Vector3(0f, 1f, 0f),
        new Vector3(1f, 1f, 0f),
        new Vector3(0f, 1f, 1f),
        new Vector3(1f, 1f, 1f),

        // Bottom Side
        new Vector3(1f, 0f, 0f),
        new Vector3(0f, 0f, 0f),
        new Vector3(1f, 0f, 1f),
        new Vector3(0f, 0f, 1f),
    };

    private static Vector3[] cubeNormals = new Vector3[]{
        // Front Side
        new Vector3(0f, 0f, 1f),
        new Vector3(0f, 0f, 1f),
        new Vector3(0f, 0f, 1f),
        new Vector3(0f, 0f, 1f),

        // Right Side
        new Vector3(0f, 1f, 0f),
        new Vector3(0f, 1f, 0f),
        new Vector3(0f, 0f, -1f),
        new Vector3(0f, 0f, -1f),

        // Back Side
        new Vector3(0f, 1f, 0f),
        new Vector3(0f, 1f, 0f),
        new Vector3(0f, 0f, -1f),
        new Vector3(0f, 0f, -1f),

        // Left Side
        new Vector3(0f, -1f, 0f),
        new Vector3(0f, -1f, 0f),
        new Vector3(0f, -1f, 0f),
        new Vector3(0f, -1f, 0f),

        // Top Side
        new Vector3(-1f, 0f, 0f),
        new Vector3(-1f, 0f, 0f),
        new Vector3(-1f, 0f, 0f),
        new Vector3(-1f, 0f, 0f),

        // Bottom Side
        new Vector3(1f, 0f, 0f),
        new Vector3(1f, 0f, 0f),
        new Vector3(1f, 0f, 0f),
        new Vector3(1f, 0f, 0f),
    };

    // Updating mesh ever frame just for convenience sake, in a game you would only want to update the mesh when you need it to change
    void Update()
    {
        MeshFilter mf = GetComponent<MeshFilter>();
        var mesh = new Mesh();
        mf.mesh = mesh;

        int sides = 6;
        Vector3[] vertices = new Vector3[sides * 4];

        Vector3[] normals = new Vector3[vertices.Length];

        Vector2[] uv = new Vector2[vertices.Length];
        int[] tri = new int[sides * 6];

        for (int i = 0; i < sides; i++)
        {
            int i4 = i * 4;

            // vertice layout
            vertices[i4 + 0] = cubeVertices[i4 + 0] * cubeSize;
            vertices[i4 + 1] = cubeVertices[i4 + 1] * cubeSize;
            vertices[i4 + 2] = cubeVertices[i4 + 2] * cubeSize;
            vertices[i4 + 3] = cubeVertices[i4 + 3] * cubeSize;

            normals[i4 + 0] = cubeNormals[i4 + 0];
            normals[i4 + 1] = cubeNormals[i4 + 1];
            normals[i4 + 2] = cubeNormals[i4 + 2];
            normals[i4 + 3] = cubeNormals[i4 + 3];

            uv[i4 + 0] = new Vector2(0, 0);
            uv[i4 + 1] = new Vector2(1, 0);
            uv[i4 + 2] = new Vector2(0, 1);
            uv[i4 + 3] = new Vector2(1, 1);

            // assign triangles to the vertices
            int i6 = i * 6;
            tri[i6 + 0] = i4 + 0;
            tri[i6 + 1] = i4 + 2;
            tri[i6 + 2] = i4 + 1;

            tri[i6 + 3] = i4 + 2;
            tri[i6 + 4] = i4 + 3;
            tri[i6 + 5] = i4 + 1;
        }

        mesh.vertices = vertices;
        mesh.normals = normals;
        mesh.uv = uv;
        mesh.triangles = tri;
    }
}