Concatenate strings in Python?

You need to add to cadena not reassign each time through the loop.

You need to also check while len(cadena + str(cadena_aleatoria(x))) as you may go over once you add str(cadena_aleatoria(x))) to cadena inside the while after your check.

while len(cadena + str(cadena_aleatoria(x))) < 256:
      cadena += clave + str(cadena_aleatoria(x))

You also need return(b) if you don't want to add None's to your cadena string

def cadena_aleatoria():
    cadena = []
    cadena.append(x)
    while len(cadena)<10:
            x = random.randint(0,9)
            cadena.append(x)
    b = "".join(str(i) for i in cadena)
    return b

def cadena_inicio():
    clave = "5275328525062135755"
    cadena = ""
    while len(cadena + cadena_aleatoria(x)) < 256:
            cadena += clave + cadena_aleatoria(x)
    print (cadena)

Your first function can be done using a list comprehension :

def cadena_aleatoria():
    return "".join([str(random.randint(0,9)) for x in range(10)])

def cadena_inicio():
    clave = "5275328525062135755"
    cadena = ""
    while len(cadena + cadena_aleatoria()) < 256:
            cadena += clave + cadena_aleatoria()
    print (cadena)

You've got a few problems.

First, you're not returning anything from the function cadena_aleatoria(x), so calling it, is returning None and you don't want to add None to your string. So if you want to return b, you should return b.

The other issue is that you're not adding any length to cadena in the while loop. You probably want to do this:

cadena += clave + str(cadena_aleatoria(x))

You're also not returning anything from cadena_inicio() but maybe this is intentional.