Yes, it is. A cubic centimetre is a measurement of VOLUME (sometimes refered to as capacity) Picture a hollow dice where the sides are each 1cm long. The dice could contain 1 cubic cm of air but it could also contain a liquid (say water) or be filled with chocolate (a solid) but the volume would still be 1 cubic cm. A cubic centimetre (or cubic anything) doesn't have to be a cube shape necessarily, any shape that holds the same amount of gas/liquid/solid as the cube is the same volume and would be classed as 1 cubic centimetre. You could be getting confused because 1 cubic centimetre is the same as 1ml and generally we refer to liquids in millilitres but they are both the same volume. It isn't incorrect to say a can of cola holds 220 cubic centimetres but usually you would say 220ml. Generally mls refer to LIQUIDS and cubic cms to SOLIDS but there's no hard and fast rule. A motorbike could be classed as 250cc. The CC stands for cubic centimetres and refers to the piston displacement.
You may also be confusing MASS and DENSITY. Using the above example the mass of the cube of water would be greater than the mass of the cube of air-tht's because the water is more dense. Think of density as how tightly packed the molecules are-the closer together they are the denser the material. So the water would be heavier (more mass) and denser than the air but they would both still be 1 cubic centimetre.
When I was a little girl my Dad used to ask me which was the heavier, a kilo of feathers or a kilo of coal? The answer is that they are both the same coz they both weigh a kilo!! But it makes you think and often catches people out. The kilo of feathers would be a lot bigger (more volume) than the coal (less volume) but both would have the same MASS (1 pound). The coal is denser than the feathers. Lead would be even denser.
People have different densities too. You could have the same VOLUME (say in cubic centimetres) as your mate but your MASS could be less. If this was the case you would be less dense than your friend.
Hope this helps
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It can be, but it depends on the scale. The volume of a room would be expressed more appropriately in cubic metres, the volume of a large lake in cubic kilometres etc. On the other hand, the volume of a raindrop could be expressed in cubic millimetres, and so on.