Answer:
336, 504
Explanation:
You want the next two numbers in the sequence beginning 6, 24, 60, 120, 210, ....
Differences
When attempting to identify a sequence it is often useful to look at the differences between terms, then at the differences of those, and so on. If The differences at some level are constant, that level tells you the degree of the polynomial that will describe the sequence. If they have a common ratio, then the sequence will be based on an exponential function.
1st differences: 18, 36, 60, 90
2nd differences: 18, 24, 30
3rd differences: 6, 6 . . . . . . . . constant, indicating a cubic function
Equation
We can go to the trouble to write four equations in the four coefficients of the cubic describing this sequence, or we can let suitable technology find it for us. The attachment shows a graphing calculator solution for the coefficients. The 10^-14 value for the 'd' coefficient is effectively 0. This value is due to the inexact representation of numbers in the floating point arithmetic used by the calculator.
The equation of the n-th term a[n] is ...
a[n] = n³ +3n² +2n
The next two terms are ...
a[6] = 336
a[7] = 540
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Additional comment
The equations for the coefficients of y = ax³ +bx² +cx +d will use the given sequence values and x values of 1..4. Here they are:
6 = a·1 +b·1 +c·1 +d
24 = a·8 +b·4 +c·2 +d
60 = a·27 +b·9 +c·3 +d
120 = a·64 +b·16 +c·4 +d
The second attachment shows a calculator solution for these four equations. (a, b, c, d) = (1, 3, 2, 0)