The program that I am using draws the cube perfectly when there is no lighting applied to the color of it. When applied it looks like it doesn't have an outer layer and the outer parts are simply non-existent. The part that is being lit up is the inside of the cube and this is very visible in the output of the program.
I tried messing around with the code itself but it doesn't seem like that is the real problem here (I may be wrong), I also tried changing the values in the position, normal and indices vectors, however, this did not yield any results either.
These are the position, normal, and index values that are used:

var positions = new Float32Array([
        // Front face
        -1.0, -1.0, 1.0,
        1.0, -1.0, 1.0,
        1.0, 1.0, 1.0,
        -1.0, 1.0, 1.0,

        // Back face
        -1.0, -1.0, -1.0,
        -1.0, 1.0, -1.0,
        1.0, 1.0, -1.0,
        1.0, -1.0, -1.0,

        // Top face
        -1.0, 1.0, -1.0,
        -1.0, 1.0, 1.0,
        1.0, 1.0, 1.0,
        1.0, 1.0, -1.0,

        // Bottom face
        -1.0, -1.0, -1.0,
        1.0, -1.0, -1.0,
        1.0, -1.0, 1.0,
        -1.0, -1.0, 1.0,

        // Right face
        1.0, -1.0, -1.0,
        1.0, 1.0, -1.0,
        1.0, 1.0, 1.0,
        1.0, -1.0, 1.0,

        // Left face
        -1.0, -1.0, -1.0,
        -1.0, -1.0, 1.0,
        -1.0, 1.0, 1.0,
        -1.0, 1.0, -1.0,
]);

var normals = new Float32Array([
        // Front
        0.0, 0.0, 1.0,
        0.0, 0.0, 1.0,
        0.0, 0.0, 1.0,
        0.0, 0.0, 1.0,

        // Back
        0.0, 0.0, -1.0,
        0.0, 0.0, -1.0,
        0.0, 0.0, -1.0,
        0.0, 0.0, -1.0,

        // Top
        0.0, 1.0, 0.0,
        0.0, 1.0, 0.0,
        0.0, 1.0, 0.0,
        0.0, 1.0, 0.0,

        // Bottom
        0.0, -1.0, 0.0,
        0.0, -1.0, 0.0,
        0.0, -1.0, 0.0,
        0.0, -1.0, 0.0,

        // Right
        1.0, 0.0, 0.0,
        1.0, 0.0, 0.0,
        1.0, 0.0, 0.0,
        1.0, 0.0, 0.0,

        // Left
        -1.0, 0.0, 0.0,
        -1.0, 0.0, 0.0,
        -1.0, 0.0, 0.0,
        -1.0, 0.0, 0.0
    ]);

var indices = new Uint16Array([
        0, 1, 2, 0, 2, 3,    // front
        4, 5, 6, 4, 6, 7,    // back
        8, 9, 10, 8, 10, 11,   // top
        12, 13, 14, 12, 14, 15,   // bottom
        16, 17, 18, 16, 18, 19,   // right
        20, 21, 22, 20, 22, 23,   // left
    ]);

Sorry for the spam of code. I can provide any more that will be necessary. The output of the program.