#### Answer

The sequence is neither geometric nor arithmetic.

#### Work Step by Step

In order to determine if the sequence is geometric, we see if the quotient of all consecutive terms is constant.
Here, we have: $\dfrac{c_{n+1}}{c_n}=\dfrac{2(n+1)^3}{2n^3}=\dfrac{(n+1)^3}{n^3}$
This shows that the quotient of all consecutive terms is not constant. Thus, it is not a geometric sequence.
In order to determine if the sequence is arithmetic, we see if the difference of all consecutive terms is constant.
Here, we have: $c_{n+1}-c_n=2(n+1)^3-2n^3=2(3n^2+3n+1)$
This shows that the difference of all consecutive terms is not constant. Thus, it is not an arithmetic sequence.
Hence, the sequence is neither geometric nor arithmetic.