Answer:
This is research work
First 10 perfect cubes since we are asking for the smallest perfect cube:
1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
5^3 = 125
6^3 = 216
7^3 = 343
8^3 = 512
9^3 = 729
10^3 = 1000
we divide 8019 by each of these perfect cubes
8019 / 1 = 8019
8019 / 8 = 1002.375
8019 / 27 = 297
8019 / 64 = 125.296875
8019 / 125 = 64,152
8019 / 216 = 37.15277777777778
8019 / 343 = 23.37900875
8019 / 512 = 15.66210938
8019 / 729 = 11
8019 / 1000 = 8.019
⇒the smallest number which, multiplied by 8019, will make the quotient a perfect cube: 27
⇒8019 divided by 27 gives an integer quotient of 297