Enabled depth buffer creates white ghost object

Hi there,

I'm "learning" opengl for some days now and try to solve all the tutorials I can find on the web.
The first "hello triangle" took quite some time, but I already got my hands on some colored cube chapters by now.

And thats where I get my first unsolvable problem (at least by me). That's why I'm here, and I hope you can help me.

--- The problem ---
When I enable the depth buffer, my code generates a strange "ghost" object after some seconds. When I disable the depth buffer, running the code won't generate it, but my cube looks wierd (because of the missing depth test).
I'm using glm for mathematics, GLEW 1.9 and GLFW 3.0.1.
For demonstration purposes, watch this short clip on youtube, to see my problem in action:

http://www.youtube.com/watch?v=TYKMR7lkp30
(Error shows up at 0:11)

--- The code ---
I know my code is not the best.
I have been coding .NET (C#) for years now and learn opengl and c++ now the "learning by doing" way for a week
I try to shorten it to the important parts:

1) Setting up the window:

	//GLFW
	if(glfwInit() == GL_FALSE)
	{
		cerr << "GLFW Init Error!";
		cin.ignore( numeric_limits<streamsize>::max(), '\n' );
		return 1;
	}
	//GLFW Hints
	glfwWindowHint(GLFW_CONTEXT_VERSION_MAJOR, 4);
	glfwWindowHint(GLFW_CONTEXT_VERSION_MINOR, 3);
	glfwWindowHint(GLFW_OPENGL_PROFILE, GLFW_OPENGL_CORE_PROFILE);
	glfwWindowHint(GLFW_OPENGL_FORWARD_COMPAT, GL_TRUE);
	glfwWindowHint(GLFW_DEPTH_BITS,32);
	//GLFW window
	GLFWwindow* w = glfwCreateWindow(SCREEN_W, SCREEN_H, "Test 01", NULL, NULL);
	glfwMakeContextCurrent(w);
	//GLEW
	glewExperimental = GL_TRUE; 
	GLenum err = glewInit();
	if(err != GLEW_OK)
	{
		cerr << "GLEW Init Error: " << glewGetErrorString(err);
		cin.ignore( numeric_limits<streamsize>::max(), '\n' );
		return 1;
	}

2) Creating the buffers and that stuff:
(The first two lines create a custom made "cube" object. The constructor takes X/Y/Z-coords in world space and the length of the cubes sides. The second line creates the vertices for the cube.)

	//Cube
	cuteCube = new cube(0,0,0,2);
	cuteCube->createCubeVertices();
	//Indices Buffer
	glGenBuffers(1, ebo);
	glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, ebo[0]);
	glBufferData(GL_ELEMENT_ARRAY_BUFFER, cuteCube->getVertexIndicesSize(), cuteCube->getVertexIndices(), GL_STATIC_DRAW);
	//Vertex Arrays
	glGenVertexArrays(1, vao);
	glBindVertexArray(vao[0]);
	//VBO Buffer
	glGenBuffers(1, vbo);
	glBindBuffer(GL_ARRAY_BUFFER, vbo[0]);
	glBufferData(GL_ARRAY_BUFFER, cuteCube->getVertexPositionsSize() + cuteCube->getVertexColorsSize(), NULL, GL_STATIC_DRAW);
	glBufferSubData(GL_ARRAY_BUFFER, 0, cuteCube->getVertexPositionsSize(), cuteCube->getVertexPositions());
	glBufferSubData(GL_ARRAY_BUFFER, cuteCube->getVertexPositionsSize(), cuteCube->getVertexColorsSize(), cuteCube->getVertexColors());
	shader_position = glGetAttribLocation(shader_program, "inPosition");
	shader_color = glGetAttribLocation(shader_program, "inColor");
	glVertexAttribPointer(shader_position, 4, GL_FLOAT, GL_FALSE, 0, (const GLvoid*)0);
	glVertexAttribPointer(shader_color, 4, GL_FLOAT, GL_FALSE, 0, (const GLvoid*)cuteCube->getVertexPositionsSize());
	glEnableVertexAttribArray(shader_position);
	glEnableVertexAttribArray(shader_color);
	glClearColor(1.0, 1.0, 1.0, 1.0);
        //MVP stuff
        shader_mvp = glGetUniformLocation(shader_program, "MVP");
	glm::mat4 Projection = glm::perspective(45.0f, (float)SCREEN_W / (float)SCREEN_H, 0.1f, 100.0f);
	glm::mat4 View = glm::lookAt(glm::vec3(4,3,-3), glm::vec3(0,0,0), glm::vec3(0,1,0));
	glm::mat4 Model = glm::mat4(1.0f);
	glm::mat4 MVP = Projection * View * Model;

3) The "render-loop":

	while (!glfwWindowShouldClose(w))
	{		
                glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
                //This line "enables" the bug
		glEnable(GL_DEPTH_TEST);
		glDepthFunc(GL_LESS);
		glUseProgram(shader_program);
		//setup uniform MVP
                glUniformMatrix4fv(shader_mvp, 1, GL_FALSE, &MVP[0][0]);
		glBindVertexArray(vao[0]);
		glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, ebo[0]);
		glPolygonMode(GL_FRONT_AND_BACK, rendermode[render]);
		glDrawElements(GL_TRIANGLES, 36, GL_UNSIGNED_SHORT, NULL);
		glfwSwapBuffers(w);
		glfwPollEvents();
		//Update rotation
		Model = glm::rotate(Model,1.0f,glm::vec3(0,1,0));
		MVP = Projection * View * Model; 
	}

4) The shaders.
4.1) Vertex shader:

#version 430 core
in vec4 inPosition;
in vec4 inColor;
out vec4 passColor;
uniform mat4 MVP;
void main()
{
	passColor = inColor;
	gl_Position = MVP * inPosition;
}

4.2) Fragment shader:

#version 430 core
in vec4 passColor;
out vec4 outColor;
void main()
{
	outColor = vec4(passColor[0], passColor[1], passColor[2], passColor[3]);
}

I am thankful for any suggestions.