Properties of cubes of natural numbers

[kpinky]

can anyone please give me whole list of properties of cubes of natural numbers Media URL: http://youtu.be/J_8xZmMqCRA
Description:

[factor-fiction]

http://youtu.be/J_8xZmMqCRA

I'm reposting the link so we can look at it

[factor-fiction]

Your link lists quite a few for starters:
(i) Cubes of all even natural numbers are even. (ii) Cubes of all odd natural numbers are odd. (iii) Cubes of numbers ending in digits 1, 4, 5, and 9 are the numbers ending in the same digit.
(iii) Cubes of numbers ending in digits 2 ends in digit 8.
(iv) Cubes of numbers ending in digits 8 ends in digit 2.
(v) Cubes of numbers ending in digits 3 ends in digit 7.
(vi) Cubes of numbers ending in digits 7 ends in digit 3.

[factor-fiction]

I had two number 3s in my list- there are 7 properties listed here. I'm sure a google search will throw up a longer list

[mike11111]

Cubes of numbers ending in 6 also end in 6.

[factor-fiction]

And of course that old favourite:
for any integer n greater than or equal to 2, n³ can be represented as the sum of consecutive (positive) odd integers.

[factor-fiction]

cubes of all numbers ending in a zero will also end in a zero

[factor-fiction]

How old is your son and what level is he studying at?
Maybe he is just expected to explore for himself by identifying some cube numbers and looking for patterns and properties.

Here's an example.
1³ = 1
2³ = 8 = 3+5
3³ = 27 = 7+9+11
4³ = 64 = 13+15+17+19
5³ = 125 = 21+23+25+27+29
6³ = 216 = 31+33+35+37+39+41

[factor-fiction]

I must stop talking to myself online

[factor-fiction]

Well, I enjoyed working on this query but it'd be interesting to know whether our answers helped kpinky's son