Answer: Option B
:
B
This question is entirely based on the powers of 2 less than 127.

Thus the answer is $2^6=64$ cubes in the cup with the most sugar.

How is that? Let us look at this important concept using the unitary approach:
Take the number 5.
In other words the question is - how many numbers would you need so that all the numbers from 1 to 5 are possible using addition.
The powers of 2 less than 5 are $2^0=1,2^1=2$ and $2^2=4$.
1= 1
2= 2
3= 1+2
4=4
5=4+1
Thus, we see that with powers of 2 we can easily write all the numbers below the highest power of 2 taken.
In case we take up to $2^2$, then we can write all values upto $2^3-1$ or 7.
$2^0=1$
$2^1=2$
$2^1+2^0=3$
$2^2=4$
$2^2+2^0=5$
$2^2+2^1=6$
$2^2+2^1+2^0=7$
Hence with 3 numbers you can write upto 7.
Hence to add up to 127 you will have to consider the powers of 2 till $2^6$.

So the cups must contain 1, 2, 4, 8, 16, 32, and 64 cubes of sugar, with 64 being the most number of cubes in one cup.