I just remembered
I've got to buy the cake
As far as i think i can't say I just remember to buy the cake
Because I remember would mean that is in my memory(that won't mean to recall, it would mean to retain or keep in memory)
(the process of remembering is now done and now I know that i have to buy the cake)
Best Answer
You can use "just" with "remember" in the present perfect or simple past to express your having just remembered:
BrE prefers the present perfect.
The simple present is impossible here. You cannot say:
I just remember to buy the cake.However, without the word "just", it would be possible to exclaim: