Learn Polish: Dzieci lubią cukierki.

Yes! The word dziecko (child) has a completely irregular plural form. Instead of following normal neuter noun rules, it changes entirely to dzieci. It is a very common word, so you just have to memorize this special plural form!

Could I use podobają się instead of lubią to say the children like sweets?

Not really. You use lubić (here in the "they" form, lubią) for things you enjoy doing, eating, or for general fondness. You use podobać się mostly for aesthetic appeal, like thinking a dress or a view is pretty. For enjoying the taste of food like cukierki, lubić is the right choice.

What case is cukierki in this sentence?

It is in the accusative case because it is the direct object of the verb lubią (they like). The singular word is cukierek, which is a masculine inanimate noun. For inanimate masculine nouns, the accusative plural looks exactly the same as the nominative plural, which is why it is cukierki.

Where did the second e go when cukierek became cukierki?