WHY a Volume of an object is proportional to ots lenght^3

I think you mean why two similar objects have volumes in the ratio which is the cube of the ratio of their lengths.

You can see the following proof by two cubes.

Suppose Cube A has length rcm, while Cube B has length krcm.

The ratio of their lengths (A to B) = r : kr = 1 : k

(1 : k)^3 = 1 : k^3

The volume of Cube A : (r)(r)(r) = r^3 cm^3

The volume of Cube B : (kr)(kr)(kr) = (kr)^3 cm^3

VA : VB = r^3 : (kr)^3 = 1 : k^3

which is the cube of their ratio of lengths.

You may also apply this to other similar solids. Hope it helps.

這不算甚麼證明吧。

正確的證明，用體積的定義為definite triple integral，用coordinate transformation去證。當然中學生就不用這麼嚴謹。

中學生的話，可以把一個物體拆成無限個很少很少的立方體來想像。