The formula that I know for correlation coefficient r:$\frac{\sum (x_i - \bar{x}) (Y_i - \bar{Y})}{\sqrt{\sum(x_i-\bar{x})^2\sum(Y_i-\bar{Y})^2}}$
If the only given values I have are $\sum x_i, \sum x_i^2, \sum y_i, \sum x_iy_i$ is it even possible to compute the correlation coefficient?
Apparently you are referring Pearson's sample correlation coefficient. In that case, one of the known alternative formulas is
$ r_{xy} = \frac{\sum x_i y_i - \sum xi \sum yi}{\sqrt{ n \sum x_i^2 - \left ( \sum x_i \right )^2}\sqrt{ n \sum y_i^2 - \left ( \sum y_i \right )^2}} $
So I believe that you would still need to have at least $\sum y_i^2$ and $n$ to compute it.