Turns out using a for loop instead of a while loop is enough to pass tests under 7s. also managed to pass with a while loop by keeping object declarations to a minimum; see reason below:
https://stackoverflow.com/questions/869229/why-is-looping-over-range-in-python-faster-than-using-a-while-loop

Added to the rounding issues one will encounter when using sqrt() for the first n cubes solution makes me wonder whether this is a kyu 6 kata for the unlucky few who draw up one of these solutions in python; just food for thought.