C++ OpenGL, GLFW Drawing a simple cube

1. You never set a (meaningful) projection matrix.
2. Abuse not the projection matrix stack.
3. Don't set your matrices in drawCube(), single responsibility principle and all that.
4. Set your viewport before trying to draw.
5. C++ has c-prefixed versions (stdio.h -> cstdio) of the C headers. Use those instead.

All together:

#include <GL/glew.h>
#include <GLFW/glfw3.h>

#include <cstdio>

void controls(GLFWwindow* window, int key, int scancode, int action, int mods)
{
    if(action == GLFW_PRESS)
        if(key == GLFW_KEY_ESCAPE)
            glfwSetWindowShouldClose(window, GL_TRUE);
}

GLFWwindow* initWindow(const int resX, const int resY)
{
    if(!glfwInit())
    {
        fprintf(stderr, "Failed to initialize GLFW\n");
        return NULL;
    }
    glfwWindowHint(GLFW_SAMPLES, 4); // 4x antialiasing

    // Open a window and create its OpenGL context
    GLFWwindow* window = glfwCreateWindow(resX, resY, "TEST", NULL, NULL);

    if(window == NULL)
    {
        fprintf(stderr, "Failed to open GLFW window.\n");
        glfwTerminate();
        return NULL;
    }

    glfwMakeContextCurrent(window);
    glfwSetKeyCallback(window, controls);

    // Get info of GPU and supported OpenGL version
    printf("Renderer: %s\n", glGetString(GL_RENDERER));
    printf("OpenGL version supported %s\n", glGetString(GL_VERSION));

    glEnable(GL_DEPTH_TEST); // Depth Testing
    glDepthFunc(GL_LEQUAL);
    glDisable(GL_CULL_FACE);
    glCullFace(GL_BACK);
    return window;
}

void drawCube()
{
    GLfloat vertices[] =
    {
        -1, -1, -1,   -1, -1,  1,   -1,  1,  1,   -1,  1, -1,
        1, -1, -1,    1, -1,  1,    1,  1,  1,    1,  1, -1,
        -1, -1, -1,   -1, -1,  1,    1, -1,  1,    1, -1, -1,
        -1,  1, -1,   -1,  1,  1,    1,  1,  1,    1,  1, -1,
        -1, -1, -1,   -1,  1, -1,    1,  1, -1,    1, -1, -1,
        -1, -1,  1,   -1,  1,  1,    1,  1,  1,    1, -1,  1
    };

    GLfloat colors[] =
    {
        0, 0, 0,   0, 0, 1,   0, 1, 1,   0, 1, 0,
        1, 0, 0,   1, 0, 1,   1, 1, 1,   1, 1, 0,
        0, 0, 0,   0, 0, 1,   1, 0, 1,   1, 0, 0,
        0, 1, 0,   0, 1, 1,   1, 1, 1,   1, 1, 0,
        0, 0, 0,   0, 1, 0,   1, 1, 0,   1, 0, 0,
        0, 0, 1,   0, 1, 1,   1, 1, 1,   1, 0, 1
    };

    static float alpha = 0;
    //attempt to rotate cube
    glRotatef(alpha, 0, 1, 0);

    /* We have a color array and a vertex array */
    glEnableClientState(GL_VERTEX_ARRAY);
    glEnableClientState(GL_COLOR_ARRAY);
    glVertexPointer(3, GL_FLOAT, 0, vertices);
    glColorPointer(3, GL_FLOAT, 0, colors);

    /* Send data : 24 vertices */
    glDrawArrays(GL_QUADS, 0, 24);

    /* Cleanup states */
    glDisableClientState(GL_COLOR_ARRAY);
    glDisableClientState(GL_VERTEX_ARRAY);
    alpha += 1;
}

void display( GLFWwindow* window )
{
    while(!glfwWindowShouldClose(window))
    {
        // Scale to window size
        GLint windowWidth, windowHeight;
        glfwGetWindowSize(window, &windowWidth, &windowHeight);
        glViewport(0, 0, windowWidth, windowHeight);

        // Draw stuff
        glClearColor(0.0, 0.8, 0.3, 1.0);
        glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

        glMatrixMode(GL_PROJECTION_MATRIX);
        glLoadIdentity();
        gluPerspective( 60, (double)windowWidth / (double)windowHeight, 0.1, 100 );

        glMatrixMode(GL_MODELVIEW_MATRIX);
        glTranslatef(0,0,-5);

        drawCube();

        // Update Screen
        glfwSwapBuffers(window);

        // Check for any input, or window movement
        glfwPollEvents();
    }
}

int main(int argc, char** argv)
{
    GLFWwindow* window = initWindow(1024, 620);
    if( NULL != window )
    {
        display( window );
    }
    glfwDestroyWindow(window);
    glfwTerminate();
    return 0;
}

I believe your problem is that you're basically using orthographic projection, or certainly something that's not perspective, which is what will give the cube more of the "3D" appearance I think you're looking for.

Try something like the following to set a correct perspective projection matrix:

glMatrixMode(GL_PROJECTION_MATRIX);
glLoadIdentity();
gluPerspective(45, windowWidth / windowHeight, 0.1f, 100.0f);

// Draw calls.