If Natural Number has 3 at one's place, Cube Number of such Natural Number also has 7 at one's place

Property 1	Property 2	Property 3	Property 4	Property 5
Property 6	Property 7	Property 8	Property 9	Property 10
Property 11

Observe the following table: Table 1 Natural Number Cube Number 1 1 2 8 3 27 4 64 5 125 6 216 7 343 8 512 9 729 10 1000 11 1331 12 1728 13 2197 14 2744 15 3375 16 4096 17 4913 18 5832 19 6859 20 8000 21 9261 22 10648 23 12167 Above table - 1 represents square of first 23 natural numbers. You must have observed that the Natural Numbers having 3 at its one's place (highlighted in yellow) and their corresponding Cube Numbers have 7 at its one's place (highlighted in green). i.e. Cube of 3 = 27 Cube of 13 = 2197 Cube of 23 = 12167 Let's try few more cube numbers as shown in table 2 and table 3: Table : 2 Table : 3 Natural Number Cube Number 43 79507 44 85184 45 91125 46 97336 47 103823 48 110592 49 117649 50 125000 51 132651 52 140608 53 148877 54 157464 55 166375 56 175616 57 185193 58 195112 59 205379 60 216000 61 226981 62 238328 63 250047 Natural Number Cube Number 83 571787 84 592704 85 614125 86 636056 87 658503 88 681472 89 704969 90 729000 91 753571 92 778688 93 804357 94 830584 95 857375 96 884736 97 912673 98 941192 99 970299 100 1000000 101 1030301 102 1061208 103 1092727 Table - 2 represents cubes of numbers from 43 to 63 Table - 3 represents cubes of numbers from 83 to 103 In these tables also you will observe the same pattern which you observed in Table 1 i.e. Natural Numbers having 3 one's place (highlighted in yellow) and their corresponding cube Numbers have 7 at its one's place (highlighted in green). So, this explains the property of square numbers that: If a Natural Number has 3 at its one's place, then the Cube Number of such Natural Numbers always have 7 at its one's place. Or we can also say that: Cubes; of Natural Numbers ending with 3, end with 7. Also we get that: If a Natural Number has 7 at its one's place, then the Natural Number is not always a Perfect Cube. e.g. 17, 67, 97 all are not cube numbers