For the linear model
$$y_i=\beta_0 +\sum_{k=1}^{n}\beta_k x_{ik} + \epsilon_i$$
the parameter estimates are the same for the maximum likelihood method and the least square method (minimizing $\sum_{i=1}^n\epsilon_i^2$) if the errors are assumed iid normal. So I am thinking that if we use least squares, we are perhaps implicitly assigning normality to the errors. Is this correct - can it be shown that the least square method does this (without appealing to the maximum likelihood solution)?