Answer
-8
Work Step by Step
We need the highest value of n to get a positive integer ending in 2
$(-n)^{3}$
To start off we need a number that has a cube ending in 2. Beetwen 0 and 9, 8 has 512 as its cube, which has 2 in the last place.
$8^{3}$=512
If we replace n for 8, the result ends up being -512 because we multiply -8 three times. Multiplying two negative numbers gives us a positive number, but multiplying that number again with a negative one gives us a negative number.
$(-(8))^{3}$=-512
That's why n has to be -8 instead of 8.
$(-(-8))^{3}$=$8^{3}$=512
