How big is a cube? Isn't that like me asking you how long my potting shed is? And don't you need topsoil? Surely compost will collapse and leave your lawn all lumpy again?

EDIT If a cube means a cubic metre then you should have the right amount. I still wish it was topsoil though.

The area of you lawn is 15 sq m - perhaps it's about 4m by 3.75m and you arrived at 15 by multiplying 3.75 and 4.

To find the volume of soil needed to lay 8cm depth over 15 sq m you need to multiply depth by width by length. 8cm is 0.08m so the sum is

      0.08 x 4 x 3.75 = 1.2

Hence the volume required is 1.2 cubic m.

1 cubic metre of anything has a volume of 1 cubic metre - it doesn't matter if it's sand or water or solid gold.