I gave a shot and I'm not sure if I got it correct by sheer luck or if my methods were correct.
Your methods are correct.
I ended up having to use a calculator at the (-8)^3 part as I wasn't sure how to solve for that in any other way than brute forcing it.
(−8)3(mod27)≡(−8)2⋅(−8)(mod27)≡64⋅(−8)(mod27)|64(mod27)≡64−2⋅27(mod27)=10(mod27)≡10⋅(−8)(mod27)≡−80(mod27)≡−80+3⋅27(mod27)≡−80+81(mod27)≡1(mod27)
