A cubic inch is a unit of volume. A centimetre is a unit of distance. The two units are therefore incompatible.
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Multiply 20 x 15 x 78 = 23400 cubic cm = 1428 cubic inches
If you multiply that, you get cubic centimeters. You can convert that to cubic inches; therefore, it doesn't make sense to convert it to linear inches.
15 cubic inches = 0.00868 cubic feet.
18" x 8" x 15" = 2,160 cubic inches = 1.25 cubic feet
154 cubic inches = 2524 cubic cm, approx.