I find the easiest method is this:
Double the first digit: 2×7=14 then subtract this from the number formed by the first two digits using decimal arithmetic: 70-14=56. Bring down the next digit 3 and double 56=112. Subtract: 563-112=451. Bring down the last digit 5 and double 451=902, so we have 4515-902=3613. The reason this works is that 8 differs from 10 by 2, hence we double. This is much easier than multiplying by 8. (10 octal is 10-2=8 decimal; 10 decimal is 10+2=12 octal.)
Another way to do this: multiply 7 by 8 and add the next digit 0: 56+0=56. Now multiply 56 by 8 and add the next digit: 451. Multiply 451 by 8 and add the last digit: 3608+5=3613.
Yet another way to do this is to use powers of 8. In the octal thousands position we have 7, so 1000 in octal is 512 decimal, multiplied by 7=3584. There are no octal hundreds so we next have 35 octal which is 3×8+5=29, added to 3584=3613.
To convert from decimal to octal we use double and add, instead of double and subtract, and octal instead of decimal arithmetic:
3613 converts like this:
Double 3 and add to 36 (octal arithmetic): 36+6=44.
Double 44=110 (not 88!) and add to 441=551.
Double 551=1322 and add to 5513=7035. Simple!
