As most soil is sold by the cubic foot (CF), it would depend on how tall your raised garden is. Assuming you use the one in the video, it is 10" tall. So, taking your 4 foot x 4 foot garden, 4 x 4 x 10/12 (to convert the 10" to feet) = 13 1/3 CF.
If you want to do the calculation in inches, 48 x 48 x 10 = 23,040 cubic inches, then divide by 1728 to get cubic feet.
I would think 13 bags of 1CF would be plenty, especially since you are displaying some soil with the plant root ball.
For me, I have used lanscape fabric as a weed block, to allow for drainage.
Hope that helps.
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