The analog is no good because it assumes people have an intuitive understanding of the volume of the Earth, which basically 0 people do because it's stupidly absurdly counter-intuitive (like volume in general). So let's go for something way smaller. Imagine we take just one little 'cube' of Earth that's just 1 mile on each side. And let's start placing boxes in it that are 1 cubic foot in size, so about the size of a micro microwave. How many of these boxes would it take to fill our little cube? The math is simple, but the answer is no less stupefying or counter-intuitive. It's more than 147 billion!!

Ok. Imagine we take those cubes that filled our 'little' cube of earth and taped them in one giant stack. That stack would not only reach to the Moon, but reach to the Moon 116 times over! In fact you'd be nearly able to reach Mars at its closest approach (34.8 million miles, vs 27.8 million miles for our box stack). And that's in 1 cubic mile of volume. The volume of Earth is about 260 billion cubic miles. To wrap up by getting back to golf balls - you can fit about 700 golf balls in 1 cubic ft.

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Actually a somewhat macabre example came to mind. How many humans could we fit in our little cubic mile? And the answer is literally all of us, many times over in fact! And that's in just one cubic mile of the 260 billion total on Earth.