Using big- O notation estimate in terms of a simple function of $ n $ the number of bit operations required to compute $ 3^n$ in binary.

I need some help with the above question. The number of bit operations required to multiply two k- bit numbers is $ O(k^2)$ . In the first step I am multiplying two 2-bit numbers, in the 2nd step a 4-bit and a 2-bit number and so on. So the total bit operations will be I feel $ O(k^2) + O(k^2 * k) +…. + O(k^{n-1} * k) \,\,with \,\, k \,= 2 $

How will the above sum be estimated as a function of n?