Let's solve each equation step by step:

1) (2x - 12) / 3 - 14) x 4 = 1000

First, simplify the expression inside the parentheses:
(2x - 12) / 3 - 14 = (2x - 12 - 42) / 3 = (2x - 54) / 3

Now, substitute this back into the equation:
((2x - 54) / 3) x 4 = 1000

Multiply both sides by 3 to get rid of the fraction:
2x - 54 = 3000

Add 54 to both sides:
2x = 3054

Divide both sides by 2:
x = 1527

Therefore, the solution to the equation is x = 1527.

2) 9 x (x - 1)^3 = 4^3 + 2^3

First, simplify the right side of the equation:
4^3 + 2^3 = 64 + 8 = 72

Now, substitute this back into the equation:
9 x (x - 1)^3 = 72

Divide both sides by 9:
(x - 1)^3 = 8

Take the cube root of both sides:
x - 1 = 2

Add 1 to both sides:
x = 3

Therefore, the solution to the equation is x = 3.

3) 105 * 5^x - 5^(x+1) = 2500

First, simplify the equation by combining like terms:
105 * 5^x - 5 * 5^x = 2500

Factor out 5^x:
5^x * (105 - 5) = 2500

Simplify further:
5^x * 100 = 2500

Divide both sides by 100:
5^x = 25

Take the logarithm of both sides (base 5):
x = log5(25)

Since 5^2 = 25, the logarithm base 5 of 25 is 2.

Therefore, the solution to the equation is x = 2.