If (a, b ∈ ℤ), then which of the following congruences holds true?
a.) ( (a mod 3)³ ≡ (a mod 3)³ mod 3 )
b.) ( (a mod 3)³ ≢ (b mod 3)³ mod 3 )
c.) ( (a mod 3)³ ≡ (b mod 3)³ mod 3 )
d.) ( (a mod 3)³ mod 3 ≠ (b mod 3)³ )