Digital Cubes


The number $153$ is equal to the sum of the cubes of its digits:
$$1^3 + 5^3 + 3^3 = 1 + 125 + 27 = 153$$
In general,
$$a^3+b^3+c^3=100a+10b+c$$
There are three other $3$-digit numbers (Digital Cubes) with the same property, excluding numbers like $001$ with a leading zero.
Do you want to try to find them?
Firstly, you may want to list all the cubes of the ten digits;
$$ 0^3 = 0, 1^3 = 1, 2^3 = 8, 3^3 = 27, 4^3 = 64, 5^3 = 125, 6^3 = 216, 7^3 = 343, 8^3 = 512, 9^3 = 729$$
The first one has already been given for you, and try open the following three remaining cubes one at a time. Have fun!

First Digital Cube Number

$1^3 + 5^3 + 3^3 = 1 + 125 + 27 = 153$

Second Digital Cube Number

$3^3 + 7^3 + 0^3 = 27 + 343 + 0 = 370$

Third Digital Cube Number

$3^3 + 7^3 + 1^3 = 27 + 343 + 1 = 371$

Fourth Digital Cube Number

$4^3 + 0^3 + 7^3 = 64 + 0 + 343 = 407$


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