To calculate \( A - B \) where:

\[
A = 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + 50 \cdot 51
\]

and

\[
B = 1^2 + 2^2 + 3^2 + \ldots + 50^2,
\]

we first need to find \( A \) and \( B \).

### Step 1: Calculate \( A \)

The term can be simplified as:

\[
A = \sum_{n=1}^{50} n \cdot (n+1) = \sum_{n=1}^{50} (n^2 + n) = \sum_{n=1}^{50} n^2 + \sum_{n=1}^{50} n.
\]

Using the formulas for the sums:

1. The sum of the first \( n \) natural numbers:
\[
\sum_{k=1}^{n} k = \frac{n(n+1)}{2}.
\]
For \( n = 50 \):
\[
\sum_{k=1}^{50} k = \frac{50 \cdot 51}{2} = 1275.
\]

2. The sum of the squares of the first \( n \) natural numbers:
\[
\sum_{k=1}^{n} k^2 = \frac{n(n+1)(2n+1)}{6}.
\]
For \( n = 50 \):
\[
\sum_{k=1}^{50} k^2 = \frac{50 \cdot 51 \cdot 101}{6} = 42925.
\]

Putting it together, we get:

\[
A = \sum_{n=1}^{50} n^2 + \sum_{n=1}^{50} n = 42925 + 1275 = 44200.
\]

### Step 2: Calculate \( B \)

As calculated before:

\[
B = \sum_{n=1}^{50} n^2 = 42925.
\]

### Step 3: Calculate \( A - B \)

Now we can find \( A - B \):

\[
A - B = 44200 - 42925 = 275.
\]

### Final Result

\[
\boxed{275}.
\]