Cambria was various cuboids from \(1\times 1\times1\) cubes. She initially built one cuboid, then increased its length and width by \(1\) and reduced its height by \(2\). She noticed that she needed the same number of \(1\times 1\times 1\) cubes to build both the original and new cuboids. Show that the number of cubes used for each of the cuboids is divisible by \(3\).