Write the unit digit in the cube of the following numbers: 19, 201, 164, 1307, 510, 35, 716.

The unit digit is $\boxed{9}$.

The unit digit is $\boxed{1}$.

The unit digit is $\boxed{4}$.

The unit digit is $\boxed{3}$.

The unit digit is $\boxed{0}$.

The unit digit is $\boxed{5}$.

The unit digit is $\boxed{6}$.

The unit digit is $\boxed{2}$.

$$
\sqrt[3]{1000} = 10
$$

$\boxed{\text{Perfect cube}}$

$$
5^3 \times 7^3 = (5 \times 7)^3 = 35^3
$$

$\boxed{\text{Perfect cube}}$

$$
(100)^2 \times 10 = 10000 \times 10 = 100000
$$

$\boxed{\text{Not a perfect cube}}$

$$
(1000)^2 = 1000 \times 1000 = 1000000
$$

$$
\sqrt[3]{1000000} = 100
$$

$\boxed{\text{Perfect cube}}$

$$
21^3 = 21 \times 21 \times 21 = 441 \times 21 = 9261
$$
The cube of 21 is $\boxed{9261}$.

$$
100^3 = 100 \times 100 \times 100 = 1000000
$$
The cube of 100 is $\boxed{1000000}$.

$$
17^3 = 17 \times 17 \times 17 = 289 \times 17 = 4913
$$
The cube of 17 is $\boxed{4913}$.

$$
11^3 = 11 \times 11 \times 11 = 121 \times 11 = 1331
$$
The cube of 11 is $\boxed{1331}$.

$$
4^3 = 13 + 15 + 17 + 19 = 64
$$
The sum is $\boxed{13 + 15 + 17 + 19}$.

$$
7^3 = 43 + 45 + 47 + 49 + 51 + 53 + 55 = 343
$$
The sum is $\boxed{43 + 45 + 47 + 49 + 51 + 53 + 55}$.

$$
8^3 = 57 + 59 + 61 + 63 + 65 + 67 + 69 + 71 = 512
$$
The sum is $\boxed{57 + 59 + 61 + 63 + 65 + 67 + 69 + 71}$.

$$
11^3 = 111 + 113 + 115 + 117 + 119 + 121 + 123 + 125 + 127 + 129 + 131 = 1331
$$
The sum is $\boxed{111 + 113 + 115 + 117 + 119 + 121 + 123 + 125 + 127 + 129 + 131}$.