101
100
1331 and 2197
Between the two numbers there are only two.
43 = 64 53 = 125 63 = 216 73 = 343
There are a total of 5 positive three-digit perfect cubes that are even. To find this, we first determine the range of three-digit perfect cubes, which is from 46 to 96. Then, we identify the even perfect cubes within this range, which are 64, 216, 512, 729, and 1000.
125,216,343,512
100
The perfect cubes between 10 and 30 are 27, which is the cube of 3 (3^3). The next perfect cube, 64 (4^3), exceeds 30, while the perfect cubes below 10 are 1 (1^3) and 8 (2^3). Therefore, 27 is the only perfect cube in that range.
1, 8, 27
Simply calculate the cubes of a few small numbers, and check which of them are in the desired range.
1331 and 2197
There are two.
The perfect odd cubes between 1000 and 3000 are the cubes of odd integers that fall within this range. The smallest odd integer whose cube is greater than 1000 is 11 (since (11^3 = 1331)), and the largest odd integer whose cube is less than 3000 is 13 (since (13^3 = 2197)). Therefore, the perfect odd cubes between 1000 and 3000 are 1331 and 2197.
Including 1, there are 21 perfect cubes between one and ten thousand. These are: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261.
13 cubes 4,9,16,25,36,46,64,81,100,121,144,169,196
There are infinitely many cubes between any two numbers - no matter how close together they are. However, there may be a more useful answer in terms of "perfect" cubes: 43 = 64 < 100 < 53 = 125 and 83 = 512 < 600 < 93 = 729 So there are 4 perfect cubes in the range - those of 5 6, 7 and 8.
The number 312 lies between the perfect cubes of 6 and 7. Specifically, (6^3 = 216) and (7^3 = 343). Therefore, 312 is greater than 216 and less than 343.