Learn Farsi: اقرار او به جرم، برای اثبات کافی بود. - His confession to the crime was enough for proof.

Esbât perfectly follows the e-C1-C2-â-C3 pattern. Its root consonants are s-b-t (related to sâbet, meaning firm or fixed). Placing them into this structure creates a noun of causation meaning to make something firm, which we translate as proof or proving.

Does eghrâr (confession) also use the "Ef'âl" pattern? The root seems short.

Yes, it is also an Ef'âl verbal noun! The root is q-r-r, meaning the second and third consonants are identical. Applying the pattern gives us e-q-r-â-r. It literally means establishing or confirming a fact, which is why it translates as confession or admission.

Why do we use the preposition be for eghrâr be jorm instead of just using an ezâfe?

Certain verbal nouns keep the prepositions associated with their verbs. Since you confess to something (eghrâr kardan be), the noun also uses be. Saying eghrâr-e jorm (with an ezâfe) would sound strangely like the crime itself is making the confession.

Can I use a compound verb like sâbet kardan instead of the noun esbât in this sentence?

Yes, you could say barâye sâbet kardan kâfi bud (was enough to prove). Using the verbal noun esbât simply elevates the register, making the sentence sound a bit more formal, which fits well with the legal vocabulary like crime and confession.