1 cube, 4 cubes used to make rostrum, 9 cubes used to make higher rostrum
Take a cube.
Add three cubes to make a rostrum.
Take five more cubes and make another rostrum.
How many cubes have you used?
Can you count them without looking?
How many are needed to make the next rostrum up in size?
How many are needed to make the 10th rostrum?
20th rostrum? 100th rostrum?
Alternatively...
1 cube, 4 cubes to make 2 by 2 "square", 9 cubes to make 3 by 3 "square"
Take a cube.
Add three more to it to make a 2 by 2 "square".
How many more are needed to make a larger square?
How many are needed to make a 4 by 4 square?
How many would be needed for a 15 by 15 square?
The 25th square? The 200th square?