Squares
Let’s take the case of squares of numbers ending with 5. Take the example 25. For finding the square, take the first digit, 2. Multiply the first digit by (first digit+1), that is, 2 x (2+1) = 2 x 3 = 6. This forms the first part of the answer. The second part is 52 = 25, Therefore, the answer is 625. You can try different two digit numbers like 15, 35, 45 and so on.
This method can be applied to numbers having more digits also. But the multiplication may be a little difficult. Take, for example, 115. The first part of the answer is 11 x (11+1) = 132. The answer is 13225.
This can be used for multiplication of certain numbers also. Product of numbers like 23 x 27, 32 x 38 etc. can be done using this method. The condition is that the sum of the last digits (3+7, 2+8) should be 10 and the first digit should be the same. Take 23 x 27. The first part is 2 x (2+1) = 6. The second part is 3 x 7 = 21. Therefore, 23 x 27 = 621. Similarly, 32 x 38 = 1216.
This method can be extended to numbers with more digits also.

I will present methods based on Vedic Mathematics by which you can do multiplication,squaring and cubing within seconds.