Answer
In order for a sequence to be geometric, the quotient of all consecutive terms must be constant.
Hence here: $\frac{c_{n+1}}{c_n}=\dfrac{2(n+1)^3}{2n^3}=\dfrac{(n+1)^3}{n^3}$, which is not constant thus it is not a geometric sequence.
In order for a sequence to be arithmetic, the difference of all consecutive terms must be constant.
Hence here: $c_{n+1}-c_n=2(n+1)^3-2n^3=2(3n^2+3n+1)$, which is not constant thus it is not an arithmetic sequence.
Hence it is neither.
Work Step by Step
In order for a sequence to be geometric, the quotient of all consecutive terms must be constant.
Hence here: $\frac{c_{n+1}}{c_n}=\dfrac{2(n+1)^3}{2n^3}=\dfrac{(n+1)^3}{n^3}$, which is not constant thus it is not a geometric sequence.
In order for a sequence to be arithmetic, the difference of all consecutive terms must be constant.
Hence here: $c_{n+1}-c_n=2(n+1)^3-2n^3=2(3n^2+3n+1)$, which is not constant thus it is not an arithmetic sequence.
Hence it is neither.