I know one can say [hundreds digit] + "cento" for centuries from the twelveth to the twentieth, e.g. "Quattrocento" for the fifteenth century. But if I want to say "Ventunesimo secolo", can I say "il Diecicento"?
No, you can't say “diecicento”. The expression “il Quattrocento” is short for “il Millequattrocento”, meaning the fifteenth century (or, more precisely, the years starting from 1400 to 1499). Usually, “il Quattrocento”, “il Cinquecento” and so on are referred to the artistic or historical peculiarities of the century: for instance, *il barocco è tipico del Seicento, ma si estende anche nel primo Settecento”.
Note that “Quattrocento” is much shorter than “il quindicesimo secolo”, one of the reasons the former may be preferred.
I don't think anybody has ever said “il Cento” for the twelfth century. Anyway, the idea is that the initial “mille” is dropped; you can't drop “duemila”, at least for the time being.
At least in theory, it wouldn't be "il Duemilacento" just as the XII is sometimes called "il Millecento"?– Charo ♦May 3, 2018 at 17:45
@Charo That would be the 22nd century.– egreg ♦May 3, 2018 at 17:50
Sorry, that's true! It would be "il Duemila" (in theory).– Charo ♦May 3, 2018 at 17:55
Usually, "il Duemila" is used to denote the year 2000 not the whole century; if you want to generically refer to the years from 2000 and above, I have heard the expression is "gli anni duemila" May 4, 2018 at 15:37