We know, a perfect cube has multiples of 3 as powers of prime factors.
Now, prime factorisation of:
A) 625=5×5×5×5 =54, which is not a perfect cube.
B) 256=2×2×2×2×2×2×2×2 =28, which is not a perfect cube.
C) 343=7×7×7 =73, which is a perfect cube.
D) 243=3×3×3×3×3 =35, which is cot a perfect cube.
Hence, option C is correct.