MFR, cultus is the perfect passive participle of colō (“till, cultivate; worship”). Latin has all different endings to signify the word's purpose in a sentence, and Latin purposes a word to carry the weight of gender, number and case. Culta would be used as one of the following:
1. nominative feminine singular of cultus
2. nominative neuter plural of cultus
3. accusative neuter plural of cultus
The nominative case of colō would decline into cultus, culti, (masculine singular and plural); culta, cultae, (feminine singular and plural); cultum, culta, (neutral singular and plural.)
The word "cult" is from the "mother tongue" if you will...derived from the Proto-Indo-European root *kʷel-
The word "occult" is from the derived from the Proto-Indo-European root *kel- and the prefix /ob/, an accusative preposition which can be used in different ways. The reason it isn't "obcult" is because people speaking Latin shortened words just like other languages do. Instead of being asked, "Where Are You Going?" I usually hear something that sounds like "where ya goin?" Latin saved the O from /ob/ and doubled the first consonant in the word. Thus, occult.
I love Latin because it takes a root and adds endings, so there are just more possibilities for nuance.