"The children are eating a cake."
Translation:Çocuklar pasta yiyorlar.
Yes - in general, if you have a plural subject which is stated, the verb can be in the singular.
"Çocuklar" already shows that it's plural so it can be "yiyor" or "yiyorlar".
On the other hand, if the subject is plural but not people, the verb should be singular (but not all Turks know about this rule, I'm told). So you would say "Bu kitaplar düşüyor" (these books are falling) rather than "Bu kitaplar düşüyorlar".
So it's just humans that even have the option of adding -lar to the verb for plural.
On the other hand, if you don't mention the subject, then you need -lar on the verb: "they are eating" could be "Onlar yiyor", "Onlar yiyorlar" or "Yiyorlar", but not "Yiyor" without the "onlar".